Officials and a Qom resident said the police had fired teargas to disperse a crowd of dervishes, or mystics, and those who had gathered to support them. They said the dervishes were armed with knives and stones.
About 200 people were hurt in the clash, one official said on Wednesday.
The fighting erupted on Monday after the Sufis refused to evacuate a suburban house where they had been congregating for dervish rites, said an official at Qom municipality who spoke on condition of anonymity.
"The violence ended and their place was knocked down on Tuesday," he said, adding the municipality had demolished the building because the Sufis had illegally turned their residential building into a centre of worship.
Sufi Muslim spirituality is tolerated under mainly Shia Iran's strict Islamic laws, although some senior religious figures occasionally call for a clampdown on its rites.
Abbas Mohtaj, the governor-general of Qom, accused the dervishes of being part of a foreign plot, but he did not explain this.
Mohtaj was quoted as saying by the Jomhuri-ye Eslami newspaper: "We did not aim to confront them at first, but when we felt that ... a plot was under way, we took steps.
"The arrogant powers are exploiting every opportunity to create insecurity in our country and (the Sufis') links to foreign countries are evident."
Mohtaj said about 200 people had been hurt and around 1000 arrested.
"The arrogant powers are exploiting every opportunity to create insecurity in our country and (the Sufis') links to foreign countries are evident.
The Sufis' mystical path to God through dance and music does not go down well with some of the most senior religious figures in the country.
Ayat Allah Hossein Nouri-Hamedani in September called for a clampdown on dervish groups in the holy city of Qom, which he called a "danger to Islam".
Some said the tensions with dervishes in Qom - 120km south of Tehran - were due to the increasing popularity of Sufism there.
"Dervishes were becoming popular in Qom and the officials wanted to crack down on them," said an employee at one of Qom's reformist seminaries.