35-year-old Mannan was a top gay rights activist and editor of the country's only LGBT magazine, Roopbaan.
The machete and gun attack took place after six men forced their way into Mannan's apartment in the capital, Dhaka.
Another person was killed, named as Mahbub Rabbi Tonoy in Bangladeshi media, and one other injured.
The attack has been strongly condemned by the US embassy, where Mannan also worked.
"I am devastated by the brutal murder of Xulhaz Mannan and another young Bangladeshi," said US Ambassador Marcia Bernicat.
"We abhor this senseless act of violence and urge the government of Bangladesh in the strongest terms to apprehend the criminals behind these murders," she added.
There has been a wave of militant attacks on secular or atheist writers, members of religious minority groups and liberal voices. At least six secular bloggers and activists in Bangladesh since 2014.
Islamic State has claimed responsibility for an attack on a university professor just two days prior to the incident, according to the BBC.
Roopbaan, a magazine first published in 2014, aims to break taboos surrounding homosexuality in socially conservative Bangladesh.
Homosexuality is technically illegal in Bangladesh and remains a highly sensitive issue in society.
A "rainbow parade" planned as part of a bigger march on Bangla New Year's Day on April 14 was canceled after police raised security concerns.