Last night, Mr Kejriwal had retweeted music director Vishal Dadlani, who said on Twitter, "Stuck between a moron and a murderer....what now, India!?"
Mr Dadlani's tweet came soon after an interview of Congress vice-president Rahul Gandhi was aired by a private TV channel, and was part of a stream of reviews on Twitter. (Rahul Gandhi accuses Narendra Modi of 'abetting' Gujarat riots)
It was an apparent reference to Mr Modi, the BJP's prime ministerial candidate and Mr Gandhi, who has not been named his party's prime ministerial candidate but is largely seen as the man who will get the job if the Congress retains power in the general elections due by May. (Will consider Prime Minister's post if MPs want: Rahul Gandhi)
The music director, a prominent supporter of Mr Kejriwal's Aam Aadmi Party, has made provocative comments before, but it is the Delhi Chief Minister's endorsement of the tweet that has raised eyebrows.
The BJP's Nirmala Sitharamam has warned the chief minister that he must be "careful about what he tweets."
"He has no business to retweet and strike this language on a public domain...he is not doing public discourse any favour," she observed.
Arvind Kejriwal, after his spectacular electoral debut in the Delhi polls last month and the announcement that his AAP will contest many Lok Sabha seats, has been seen as a possible challenger to the two seasoned politicians. (One month of Kejriwal's government: 5 hits, misses)
His one month in office, which he marks today, has seen more controversy. The 33-hour protest in the heart of Delhi and his staunch defence of his law minister Somnath Bharti, who has been accused of vigilantism and of being racial and sexist, have earned Mr Kejriwal criticism. (Aam Aadmi Party completes one month in government: Rate its performance)
In yesterday's interview, Rahul Gandhi said his Congress had offered support to the minority Kejriwal government in Delhi to see how it would prove itself.
Mr Gandhi also accused Narendra Modi's government in Gujarat of "abetting" the communal riots of 2002. Mr Modi's political rivals have long alleged that he allowed or actively encouraged the attacks. He has always denied this, and a Supreme Court inquiry found no evidence to prosecute him.