Mohammad Nasir, a leader of the Jamayetul Mujahideen, was among the latest of 169 people from towns and cities across Bangladesh arrested since the blasts on 17 August, officials said.
"We arrested Nasir, one of the leading figures (of the Jamayetul Mujahideen), in Khagrachhari (on Sunday)," Home Ministry spokesman Mohammad Mohsin announced.
Khagrachhari is in the south of the country.
"We hope to get some information from him," Mohsin said, declining to elaborate.
Mohsin said six Jamayetul Mujahideen members had confessed to their direct involvement in the blasts "but they were mainly base-level workers."
A total of 434 small bombs exploded in all but one of the country's main towns and cities, killing three people and injuring more than 100.
The toll rose after one of those injured in the blasts, who was detained by police as a suspect, died of his injuries in a Dhaka hospital on Sunday.
Leaflets bearing Jamayetul Mujahideen's name and calling for the introduction of Islamic law were found at the blast sites.
Still at large
The group's top leader, Shaikh Abdur Rahman, is still in hiding.
Police last week charged him in absentia with masterminding the attacks, and a warrant has been issued for his arrest.
Police are also looking for Siddiqul Islam, also known as Bangla Bhai, the leader of the Jagrata Muslim Janata Bangladesh.
Police say it is a sister organisation of Jamayetul Mujahideen.
Both groups, which want secular Bangladesh to adopt strict Islamic law, were outlawed in February after being linked to a wave of bombings at Muslim shrines, musical events and other targets.