Before flying out on Friday night, he said he is 'not sick, but embarrassed' at the criticism by the ruling Awami League.
He says Prime Minister Sheikh Hasina may have 'felt hurt' because 'a quarter misinterpreted the verdict to her'.
Justice Sinha, whose tenure is ending on Jan 31 next year, has also warned against government 'interference' in the Supreme Court, saying it 'will not do any good' to the country.
He left Dhaka on Singapore Airlines' flight SQ 447 at 11:57pm. He will stay with his daughter Suchana Sinha in Australia, Supreme Court officials had said earlier.
Though it had previously been stated that his wife, Sushama, would travel with him, she only accompanied him to the airport.
Later, High Court's Protocol Officer Abdul Warres told bdnews24.com that she came to see Justice Sinha off.
Warres also said the chief justice's luggage include two medium-sized suitcases and a small carton.
The airlines' Duty Manager Md Zuanid Hossain said the flight departed on time. "The chief justice was alone. His wife was not with him," he added.
The plane is expected to reach Singapore at 6am local time. It will fly again for Australia after a 45-minute stopover.
No other chief justice in Bangladesh has faced such public discussion and criticism while in office as Justice Sinha.
And his trip at this time has given rise to swirling speculations and drawn huge media attention.
Referring to a letter from the chief justice to the president, Law Minister Anisul Huq said on Thursday that Justice Sinha wanted to return on Nov 10 after visiting Canada, the US and the UK besides Australia.
The president earlier accepted Justice Sinha's sick leave from Oct 3 to Nov 1. The leave was extended to Nov 10, according to an executive order issued on Thursday.
It states that Justice Abdul Wahhab Miah will stand in as chief justice between Nov 2 and Nov 10, or until Justice Sinha returns.
A dramatic turn of events
>> Reporters started to gather in front of Justice Sinha's official residence at Hare Road in the morning after hearing from the law minister on Thursday that the chief justice was leaving on Friday.
>> In the afternoon, Justice Sinha's relatives, including his sister, a cousin, and niece's husband, came to visit him.
>> The chief justice's personal and protocol vehicles were taken to the house in the evening.
>> His Personal Assistant Md Anisur Rahman entered the house around 6:45pm.
>> High Court Protocol Officer Warres told bdnews24.com by telephone at 7pm that he came to the house to get the chief justice's luggage to the airport.
>> Rasheda Sultana, the chief security officer at the airport, confirmed the chief justice's flight schedule to bdnews24.com.
>> Sabbir Faiz, an additional registrar at the High Court, entered the house around 9pm.
>> When the chief justice started for the airport at 9:56pm, over 100 media workers were there in front of the house.
The chief justice waved to the reporters from the car. His wife Sushama was beside him.
>> The chief justice came out of the car when the journalists asked him to say something about the ongoing situation in a rare event as journalists in Bangladesh rarely get the opportunity to speak to the chief justice publicly.
The chief justice said:
"I am not sick. I am well.
"I am not fleeing. I will return. I am a bit embarrassed.
"I am the guardian of the judiciary. I am leaving temporarily for the sake of the judiciary, so that its image does not get hurt. I will return.
I am not disappointed with anyone. I strongly believe that the government has been misled."
>> After delivering the short speech, he took out a piece of paper from his pocket and held it up in front of the media, saying it's his statement.
>> Just before getting in the car, he turned to the reporters again and said, "I am not leaving under pressure. I am leaving on my own."
>> His motorcade started for the airport at 9:56pm. The motorcade included three other cars with some judges on board.
>> The chief justice entered the VIP lounge at the airport at 10:40pm. His luggage were put on the conveyer belt earlier, officials said.
>> He boarded the plane at 11:49pm and it took off after eight minutes.
Two and a half months of tug-of-war
Chief Justice Sinha has been facing intense criticism by the ruling party leaders since the publication of the full appeals verdict in early August upholding the High Court judgment that scrapped the 16th constitutional amendment.
His observation on Bangladesh's politics, past dictatorships, electoral commission, corruption, governance and the judiciary in the 799-page verdict sparked sharp reactions.
Even Prime Minister Sheikh Hasina criticised the chief justice over the verdict.
Many of the Awami League leaders demanded his resignation accusing him of 'belittling' the Father of the Nation Bangabandhu Sheikh Mujibur Rahman in the observations.
Introduced by the Awami League government in 2014, the amendment restored parliament's powers to sack top court judges on grounds of incompetence and misconduct.
The BNP had welcomed the verdict, which restored the Supreme Judicial Council provision in the Constitution, a system introduced during the party founder Ziaur Rahman’s military rule to sack top court judges.
It maintains that the government forced Justice Sinha to go on the leave and travel abroad – an allegation the government denies.
Law Minister Anisul Huq publicised Justice Sinha's letter to the president seeking the leave on Oct 4, a day after it started.
In the letter, Justice Sinha asked for the leave citing complications following his longtime treatment for cancer.
Later, he wrote to the president again informing him that he planned to travel with his wife to Australia where their eldest daughter lives.
On Thursday, the law minister said the government only followed Justice Sinha's wish in issuing the executive order on the leave, its extension and his going abroad.
Amid this war of words between the Awami League and the BNP, Justice Sinha expressed his thoughts in the rare statement before the departure.
He wrote in the statement: "I am fully well, but I am truly embarrassed at how a political quarter, lawyers, and especially some honourable ministers in the government, and the honourable prime minister have criticised me personally."
He has also expressed concern over the law minister's comment that Justice Abdul Wahhab Miah, who is acting as chief justice in his absence now, is going to bring some administrative changes to the Supreme Court.
Justice Sinha says such deeds will be construed as government 'interference' in the apex court’s workings, which will 'do no good' to Bangladesh.