The workers of different opposition parties supporting the campaign launched by Telangana Joint Action Committee (TJAC) were also present during the demonstration.
Police said they are verifying reports that four persons were injured in the scuffle, which led to tension in the area.
Following the clash, police cane-charged the gathering to disperse the protesters.
The 'Dharna Chowk' is a popular place for holding demonstrations in the city.
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The residents of the adjoining areas along with the Indira Park Morning Walkers Association had opposed the TJAC's campaign, stating that the protest caused inconvenience to them.
"Following heated arguments, the two groups clashed by throwing chairs at each other," Deputy Commissioner of Police (Central Zone) D Joel Davis said.
"Violence broke out after a large number of protesters, who had assembled as part of a protest call opposing shifting of 'Dharna Chowk', tried to go at the site, and clashed with another group seeking to shift the 'Dharna Chowk'," he said.
"We are verifying on how many people were injured. Cases will be booked accordingly," he said.
As part of the 'Save Dharna Chowk' protest call, the members of TJAC and opposition parties, including the Left, Congress, TDP, BJP, besides Telugu film star Pawan Kalyan's Jana Sena holding placards, marched towards the Indira Park and raised slogans against the government.
They alleged that the ruling TRS government was adamant on shifting the 'Dharna Chowk' and "suppressing" the democratic rights of people's organisations and Opposition parties to express their views on its policies.
The Hyderabad police commissioner had earlier granted permission to both the groups to hold protests today at the 'Dharna Chowk'.
Pawan Kalyan earlier said that, "Dharna Chowk has been a great venue for people to voice their protest for decades. Now, it is no longer available for expressing their anguish and sufferings. Keeping it away (shifting the site) is not democratically correct."
Dharna Chowk, like Jantar Mantar in New Delhi, is a democratic space to voice anguish, he had said.
A couple of months ago, the TRS government disallowed protests at the chowk, saying they caused inconvenience to residents of the locality, and suggested an alternative site.