The incident took place at about 1:30 pm when committee members of the mosque were installing a water kiosk beside it, which was opposed by members of another community, leading to a clash between the two sides, District Magistrate Navdeep Rinwa said.
The argument over the kiosk led to pelting of stones from both sides. Two motorcycles were also torched, police said.
Two persons identified as Aamir and Saurabh have been injured in the violence and admitted to a hospital, Rinwa said.
Tension later spread to other areas from where stone-pelting incidents were reported, the District Magistrate said, adding the situation is tense but under control.
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About 800 Rapid Action Force personnel have been deployed along with police forces in the city's sensitive areas, he said.
Rinwas said he, along with SSP Onkar Singh, was patrolling the city in a bid to normalise the situation and a meeting between the two groups will be called to find an amicable solution to the issue.
City SP Om Prakash said people involved in the incident would be identified and arrested once the situation normalises.