Media reports said the video that went online last week was filmed in Morocco and showed three masked men holding the IS flag and introducing themselves as soldiers of the Islamic State.
The video purported to announce the creation of "Jund al-Khilafa" or soldiers of the caliphate, in the Maghreb.
The interior ministry said three people were arrested in connection with the video on Saturday and three more on Sunday.
Signup to our newsletter and follow us on Facebook and Twitter!
A statement did not identify the suspects but said the head of the group and two of his accomplices "were jailed in 2008... for their involvement in terrorist plots" and links with Al-Qaeda in the Islamic Maghreb.
A cell phone used to film the video was seized by security forces and police, as was a blade one suspect held while all three were "pledging allegiance to (IS chief) Abu Bakr al-Baghdadi", it said.
According to the interior ministry, the suspects also "threatened to carry out criminal acts" in Morocco after undergoing military training at IS camps in Libya, Syria and Iraq.
Morocco has announced the arrest of several would-be jihadists in recent weeks, and last month it boosted security across the kingdom to counter any threat.
Authorities say that more than 2,000 Moroccan jihadists, including some with dual nationality, are now fighting in Syria and Iraq where IS has set up a caliphate in territory it controls.