At least 27 people were killed and up to 200 injured in the attack.
State television is reporting the owner of the vehicle used to take the bomber to the mosque has been detained. However the driver is said to remain at large.
At least three others arrested are suspected of having ties with the attacker.
ISIL claims responsibility
The militant group calling itself Islamic State (IS) has claimed responsibility for the bombing, which is the Gulf Arab country’s worst militant assault in years.
One week into the Muslim holy month of Ramadan, worshippers were reportedly kneeling in prayer when the bomber walked in and detonated his explosives.
Government officials claim the attack was intended to stir up bad feeling between Kuwait’s Sunni majority and Shi’ite minority.