Those detained include Rajkot West Congress candidate Rajyaguru, Rajkot East Congress candidate Mitul Donga and another party worker, the police said. The three have been let off today.
Police also indulged in baton charge to disperse the mob.
Vijay Rupani is contesting polls from his Rajkot West seat against Mr Rajyaguru. Elections will be held in Rajkot on December 9.
"Scuffle broke out between Congress and BJP workers over the issue of tearing of posters. Brother of Rajyaguru, Deep was injured in the the scuffle," Joint Commissioner of police Dipak Bhatt told reporters.
Injured Congress workers were taken to City private hospital.
"Rajyaguru with a large group of Congress workers rushed to the residence of Rupani. We tried to reason it out with him but they wanted to take law in their hand," Mr Bhatt said.
"We have detained three people so far", he said adding that they used necessary force to control the situation.
Mr Rupani was at his residence when the incident took place.
Heavy police security has been put in place at the residence of the chief minister.