The arrest of Farabi Shafiur Rahman came four days after attackers wielding meat cleavers killed
Avijit Roy as he walked with his wife on a crowded pavement in the capital Dhaka on February 26.
A spokesperson for the anti-crime Rapid Action Battalion said Farabi was arrested at a bus stop.
Mufti Mahmud Khan, the spokesperson, said Rahman had made death threats against Roy, adding that a case has been filed against Farabi, and that he would be handed over to the police
"The mystery will be revealed after the interrogation," Khan said.
Rahman, a Muslim blogger who denounced atheism, had threatened Roy in Facebook postings, Khan said, quoting him as writing: "Avijit Roy lives in America, so it's not possible to kill him right now. But he will be killed when he comes back."
Responding to his posts against "atheists", most of Farabi's followers said they ought to be killed to protect Islam.
While Rahman acknowledged making the threats, Khan said, authorities refused to say if they believed he was one of the attackers.
Roy, a Bangladesh-born engineer with American citizenship, was an outspoken atheist and critic of the intertwining of religion and politics.
He was killed while on a visit from Georgia in the US to attend Dhaka's main book fair.
He and his wife, Rafida Ahmed, were attacked after leaving the fair. Ahmed was seriously injured.
Rahman had been arrested previously for threatening an imam who performed funeral prayers for another atheist Bangladeshi blogger killed in 2013.
He was released on bail after six months in jail.
The Bangladesh government has accepted a US offer of FBI help in the investigation of the killing, according to AH Mahmood Ali, the foreign minister.
With reporting from Mahmud Hossain Opu from Dhaka.
Source: Al Jazeera and agencies