The Army of Islam is influenced by al-Qaeda
Hamas said Khattab al-Maqdisi was seized in a gun battle in Gaza City. It also said the Army of Islam later kidnapped 10 Hamas university students.
The Army of Islam, a small armed group, claims to have abducted the BBC's Alan Johnston in Gaza on 12 March.
The BBC is due to hold a rally for Mr Johnston later on Monday to mark the 16th week since his disappearance.
Hamas spokesman Sami Abu Zuhri said Mr Maqdisi was detained after he opened fire on members of Hamas's self-declared police.
He said Hamas would investigate claims by the Army of Islam that Mr Maqdisi was injured during the arrest.
The spokesman also accused the clan which allegedly controls the Army of Islam of abducting 10 Hamas students.
Tensions between Hamas and the Army of Islam have been growing since Hamas seized control of the Gaza Strip last month, defeating members of another Palestinian group - Fatah.Hamas has demanded that the Army of Islam release Mr Johnston, threatening to "use all means to secure his life and to free him".
UPDATE 7/2/07 3pm: Here's a link to the NYTimes article on this, which also has information on Israel's arrest of Hamas agents in East Jerusalem: Hamas Makes Arrests in BBC Reporter’s Case