Communist Party of India (Marxist) leader Mohammad Salim said Jyotipriya Mullik’s utterances were “ridiculous”.
Mr Mullik made the controversial statement at a meeting of 2,000 party workers on Sunday.
The state government, led by Chief Minister Mamata Banerjee, has sparked a number of controversies.
The 10-month-old government’s list of “don’ts” is long and has attracted severe criticism.
Last week, police arrested a professor for allegedly posting on the internet cartoons ridiculing Ms Banerjee.
Professor Ambikesh Mahapatra of Jadavpur University was later released on bail.
The minister later told the BBC that he had only requested the party members to stay away from their political rivals.
When asked whether his call amounted to socially boycotting the Communists, Mr Mullik said: “I can’t give a call to socially boycott them. I have made a request to ‘mentally boycott’ them.”
The chief minister, who came to power in 2011 bringing to an end the state’s 34-year-old Communist rule, has attracted a lot of negative publicity.
The government was severely criticised for arresting Prof Mahapatra for allegedly circulating a cartoon criticising the chief minister.
The government has also been criticised for the forceful eviction of slum dwellers in Calcutta and the arrest of a professor who joined a demonstration against the evictions.
The state was also accused of trying to muzzle the independent press when it chose only pro-government newspapers for state-funded libraries.
Ms Banerjee’s order to paint the city blue has also been widely ridiculed.