Surjit Mathur, a member of Hindu Janajagruti Samiti (HJS), filed the complaint at Ponda police station near here yesterday.
Varma triggered a major controversy yesterday with a string of tweets about the elephant-headed God. The 52-year- old producer-director, who apart from questioning the ability of Lord Ganesh to remove obstacles from the path of his devotees, made fun of his physical attributes.
As his twitter posts triggered an outrage, Varma took to the microblogging website to tender an apology.
Investigation into the matter is on and based on the finding a decision will be taken on filing an FIR, he added.