The first FIR was lodged at Ghatlodia police station here by Vishwa Hindu Parishad activist Raju Patel, while the other was filed by Kirit Mistry at C Division police station in Bhavnagar.
Further, an application seeking legal action against her was filed at Gomtipur police station here by a Shiv Sena worker Jitu Solanki.
Setalwad had yesterday tweeted a photo-shopped picture showing, among other things, ISIS terrorists with the American journalist James Foley just before his beheading.
Inspector A G Gohil of Ghatlodia police station told PTI that Setalwad had been charged with various offences under the Information Technology Act and Indian Penal Code sections 153(a) (promoting enmity between two religious groups) and section 295 (a) (outraging religious feelings).
As per the FIR filed here, "the photo showed a member of minority community with the Sudarshan Chakra while another photo showed a terrorist beheading a journalist. This act by Setalwad has hurt the religious sentiments of Hindus".
Setalvad, on the other hand, apologised today on her blog as well as on Twitter.
"Sincere apologies for inadvertent tweet," she tweeted.
"The moment I realised that the illustration had created a controversy and had hurt many people, I deleted the tweet for having inadvertently hurt their feelings," she wrote on her blog.