The complaint was filed by RTI activist Asad Patel at the Amboli police station in Jogeshwari (West) here on Wednesday. A copy of the complaint is being circulated in the media.
"Model Sofia Hayat ne kya Hindu Muslim dharm ka mazak udaya. Amboli Police station mein complaint dakhil (Why has model Sofia Hayat made fun of Hindu and Muslim community. Complaint lodged in Amboli police station)," Patel tweeted.
She also got a Islamic moon inked.
According to the complaint copy, Sofia has disturbed the "public peace and public tranquility and public order" by getting the swastika inked on her feet.
In a statement issued on her behalf after the police complaint, Sofia said: "If they don't recognise it is sacred, then they themselves do not recognise divinity. Go arrest Buddha! I am as sacred as him. More than being religion, Hindu and Islam are a way of living life. I know who I am and what I do. Religious sacred sentiments are personal.
"No one has the right to judge. Even I as the sacred mother, do not judge. Anybody who is trying to take away these sentiments and get hurt is only reflecting negative traits in themselves which is not belonging to a divine cause."
Sofia, who has appeared in Indian TV shows like "Welcome - Baazi Mehmaan Nawazi Ki", "Bigg Boss 7" and "Comedy Nights Bachao", said she considers all religions equal.
"Feet are holy. My heart is holy. Every part of me, and indeed you, is so sacred. I wait for the day these people turn their hearts back to love of all free of judgement, fear and hate, and recognise all as one," she said.
Sofia had shared a photograph of her feet with the swastika tattoo on Instagram earlier this week. As the symbol is considered sacred by the Hindu community, Sofia courted outrage over social media.
She later took a stand for herself and wrote: "May those with anger know that they only do the work of the devil in their anger. May those that say unkind words know that those words come from negative entities whether you call it an energy, the devil or anything else."