"Since he is a part of the government, he should have given the suggestion to the government rather than making such a statement in public. Party forum is also open for suggestions," party spokesperson Rashid Alvi said.
"It would have been better if he had given this advice to the government, as after all, the decision has to be taken at their level and Home Minister (Sushilkumar Shinde) has to take the decision," he added.
The reprimand comes after Mr Tharoor tweeted yesterday to say, "Wondering what interest is served by continuing anonymity of #DelhGangRape victim. Why not name & honour her as a real person w/own identity?"
"Unless her parents object, she should be honoured & the revised anti-rape law named after her. She was a human being w/a name, not just a symbol," he said.
The minister was referring to the case of a young medical student who died over the weekend from horrific injuries after she was raped on December 16 by six men who also struck her over and over with an iron rod on a bus in Delhi.
The student's family today said that they would like her name to be used for a good cause - like tougher anti-rape laws, or a hospital in the part of Uttar Pradesh that her family belongs to.
Mr Tharoor in 2009 provoked a 'Tweet-troversy' when he referred to economy class travel as "cattle class," described by many as a condescending remark about millions of Indians who fly coach.
Before the elections in Gujarat this year, he tweeted "my wife is priceless" after Gujarat Chief Minister made derogatory remarks about his wife, Sunanda Pushkar Tharoor, describing her at a campaign rally as Mr Tharoor's "50-crore girlfriend."