Soheil Latif, a former air force officer, landed the helicopter on the field of a school inside the prison complex at Gazipur on Thursday morning.
The helicopter was rented to fly a Malaysian citizen of Bangladeshi origin and his family to a wedding in Konabari.
Its pilot left the premises immediately after 'mistakenly' dropping off the family members.
Prison authorities released the man, his wife and children after questioning.
"Meghna Aviation and its pilot will be asked to respond to our show cause notice which we will issue after consulting our superiors," said Anwar Hossain, jailor of Dhaka Central Jail-2.
The helicopter had permission to land in Kuddusnagar of Konabarhi and a police team was waiting in the location, said Inspector Mobarak Hossain, in-charge of the Konabari Police Outpost.
The pilot mistook the area inside the prison complex for Kuddusnagar, he said.
"Once in Dhaka, he realised his mistake and emailed an apology to the jail superintendent."