Awami League General Secretary Obaidul Quader disclosed Hasina’s decision to the media on Monday.
"The prime minister has instructed me to inform State Minister for Information Murad Hassan to submit his resignation by tomorrow," he said.
The 47-year-old has been in the eye of a social media storm for his untoward remarks on former prime minister Khaleda Zia's granddaughter, prompting calls from the BNP for his resignation.
Amid the furore, an audio clip of a telephone conversation began to circulate on Facebook. In the audio record purported to have his voice, Murad was heard using a stream of obscene words and threatening to drag an actress into a five-star hotel and rape her.
Actress Mahiya Mahi later took to social media and confirmed that it was her in the phone conversation with Murad. The conversation took place two years ago, according to her.
In a video uploaded on Facebook, the actress, who went on an Islamic pilgrimage to Saudi Arabia, said she was a “victim of circumstances”.
“The person who embarrassed me so much has received what he deserves,” she said, effectively calling Murad’s departure in disgrace from the cabinet a divine punishment.
She also said she was trying to avoid Murad’s indecent proposal in the phone call and was lost for words to protest the vulgar language.
Murad has not commented on the matter.
A doctor by training, Murad was elected to parliament from Jamalpur-4 for the second time in the 2018 general election.
He was initially inducted into the cabinet as the state minister for health after the election but was transferred to the information ministry four months later in May 2019.
He earned his medical degree from Mymensingh Medical College and had served in various roles, including as president, at the institution's Bangladesh Chhatra League unit, according to his biography on the information ministry's website.
However, BNP Secretary General Mirza Fakhrul Islam Alamgir on Monday claimed that Murad had once been a member of Chhatra Dal, the party's student affiliate.
"This is unfortunate. He was the publicity secretary of the Mymensingh Medical College [Chhatra Dal unit]. He later joined Chhatra League. Shame on him," he said.
Despite several attempts, Murad could not be reached for comment as his phone was switched off.