The 41-year-old British actress-model and Nayar, a 42-year-old Indian businessman, were married in a lavish Hindu ceremony at a palace-turned-hotel in the western Indian city of Jodhpur in March.
The couple first wed in a private civil ceremony in a castle outside London.
"This was a marriage for commercial purposes, but at the cost of religious feelings," Hasti Mal Saraswat, said in his complaint, The Times of India newspaper said. Saraswat is acting on behalf of Vishnu Khandelwal, a local businessman and religious activist.
Jasraj, a Hindu priest who uses just one name, also said that since the couple already had married before, they had no Hindu religious sanction to marry for a second time.
Photos: Wedding Vows In India
The complaint goes on to say that Hurley did not remove her footwear while walking around the sacred fire at the ceremony and wore revealing clothes.
The report had no details on when the complaint was likely to come up before a judge. India's legal system, burdened by a huge backlog of cases, is notoriously slow and it can take months and even years before complaints come up for hearing.
The petition was filed under a section of the Indian Penal Code that makes it an offense to upset any religious feelings with "deliberate and malicious intention."
Saraswat told the newspaper that Arun Nayar's father, Vinod Nayar, also will testify against the couple. Earlier this week, tabloids in England and India carried reports that Vinod Nayar has severed ties with his son after he was thrown out of the wedding on Hurley's urging.
Hurley and her husband have not commented on the reports or on the complaint.
Actress Hurley appeared in "Austin Powers: International Man of Mystery" and "Bedazzled," and for several years was the international face of Estee Lauder cosmetics. Her 4-year-old son, Damian, accompanied the couple on their trip to India.