"Some rogue elements and agents of the enemy who want to divide Muslim brothers sought to create insecurity in some spots in Zahedan," deputy police chief Ahmad Reza Radan told the Mehr news agency.
Those arrested "are both Sunni and Shiites and they sought a Sunni-Shiite divide," Radan said.
The city was the scene of a powerful bomb attack on a Shiite mosque on Thursday which killed 25 people, one of a number of violent incidents to shake Iran in the run-up to the June 12 presidential election.
Mehr also said some public places in Zahedan had been damaged by vandals, but gave no further information.
Radan said security had been restored on Sunday and a number of people arrested, without giving figures.
Zahedan is the capital of Sistan-Baluchestan province, which borders Afghanistan and Pakistan and has a sizeable Baluch minority who adhere to Sunni Islam.
Thursday's bombing was reportedly claimed by the shadowy Sunni rebel group Jundallah (Soldiers of God) which is blamed for much of the unrest in the province.
Iran on Saturday hanged three people for their role in the attack.
In another incident in Zahedan, gunmen on motorbikes fired at an election campaign office of President Mahmoud Ahmadinejad on Friday, wounding two campaign members and a child.
And on Saturday, Iranian security forces defused a bomb found in a toilet of a plane flying from the oil-rich city of Ahvaz to Tehran.
Ahmadinejad is running for another four-year term in the June 12 vote but faces challenges from three other candidates.
