Afghan intelligence services say they are part militant group Fedai Mahaz, which roughly translates as the Suicide Front.
Fedai Mahaz has previously claimed it was behind the murder of Nils Horner in March 2014, news agency Reuters reports. At the time, the group said it had killed a man it claimed was a British spy. There is no evidence of a link, however.
Horner, who held both Swedish and British citizenship, was killed while conducting an interview on a street in the Kabul district of Wazir Akbar Khan.
There is only vague information about the men's arrest and about the militant group.
"We still know very little about what has happened but of course we sincerely hope that the right person or people will be held responsible for the terrible murder," Anne Lagercrantz, head of Swedish Radio News, said.
The intelligence service denied earlier reports that the leader of the group had been arrested, and add that the arrests are not linked to the investigation into Nils Horner's murder.