Xulhaz Mannan, editor of a magazine for Bangladesh's gay and lesbian community, and fellow activist Mahbub Tonoy were murdered in a Dhaka apartment last month by at least six men carrying machetes and guns.
Gay rights activist among two hacked to death in Bangladesh
Police said the unnamed man was a member of a local 'Islamist' militant outfit, which has been blamed for a string of similar gruesome murders of secular and atheist bloggers.
"We've arrested one man in connection with the murder of Xulhaz Mannan," Dhaka police spokesman Maruf Hossain Sorder told AFP.
"He is a member of the Ansarullah Bangla Team," Sorder said in brief comments ahead of a press conference by top officers.
Washington has condemned the killings of Tonoy and Mannan, who worked for US government aid organisation USAID. Both men had received threats from radicals over their championing of gay rights.
Bangladesh Sufi Muslim killed in suspected extremist attack
The arrest comes after an elderly Buddhist monk was found hacked to death on Saturday in a temple in the southeastern district of Bandarban -- the seventh such killing since the start of last month.
Suspected extremists have been blamed or claimed responsibility for the scores of murders carried out since last year, as fear grips the Muslim-majority nation over the rising violence.
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