Harbhajan, who is popular in cricket circles as 'Bhajji', and his dance partner Mona of "Jassi Jaisi Koi Nahin" fame, had last week performed a number on dance reality show "Ek Khiladi, Ek Hasina" depicting themselves as mythological demon-king Ravana and Lord Ram's wife Sita.
Gurbachan Singh, the acting head of the Akal Takht, has taken strong exception to the depiction of Hindu gods by the two celebrities, who incidentally, are both Sikhs.
"Though I have not received a complaint in this regard, I think it is unreasonable to mock at religious deities like this. Ravana is known as evil. How can Ravana and Sita dance together? That the dance was done by two Sikhs is condemnable, " the Akal Takht chief said.
He added that if any complaint in this regard was made to him, he would inquire into it and initiate religious action against the erring stars.
Shiromani Gurudwara Prabandhak Committee (SGPC) president Avtar Singh Makkar said that celebrities should desist from such acts as they are role models for millions of fans.
Radical Hindu organisations have also objected to the dance number that allegedly mocked Hindu sentiments. In Hindu mythology, Rama's wife Sita was abducted by demon-king Ravana.
"We should show respect to all religions and their entities. If we cannot tolerate anything against our religion, how can we mock at others?" Gurbachan Singh said.
Harbhajan has been mired in several controversies in recent months including his on-field spat with Australian all-rounder Andrew Symonds and opener Mathew Hayden.
He was also involved in a 'slapgate' controversy with Indian teammate and fast bowler S. Sreesanth when he slapped the latter after losing a match in the multi-million dollar Indian Premier League (IPL) tournament.