Police say Rafiqul Islam, 30, attacked her because she pursued higher education without his permission.
They say Mr Islam, a migrant worker, admitted to the crime shortly after returning home from the Gulf.
The incident is one of a number of acts of domestic violence targeting educated women in recent months.
Police say that Mr Islam, who works in the United Arab Emirates, tied up his 21-year-old wife, Hawa Akther Jui, earlier this month. He then taped her mouth and cut off the five fingers.
Doctors say the fingers cannot be re-attached and it appears that Ms Akther will have to live with permanent disfigurement.
“After he came back to Bangladesh, he wanted to have a discussion with me. Suddenly, he blindfolded me and tied my hand,” Ms Akther told the BBC from the town of Narsingdi.
“He also taped my mouth saying that he would give me some surprise gifts. But, instead he cut off my fingers.”
“Doctors said my fingers could be re-attached within six hours but he refused to give them.
The police officer investigating the case, ARM Al-Mamun, said “preliminary investigations” had led police to believe that it was a “pre-planned attack”.
The attack follows an incident in June in which a university lecturer lost one eye while the other was badly wounded in an attack allegedly carried out by her husband.