The Asian Civilisation Museum (ACM) bought the artwork for $650,000 (£420,000) from New York dealer Art of the Past in 2007.
The company's manager later admitted selling stolen Indian antiquities, including the bronze being returned.
The allegations first came to light during a 2012 court case against the firm for trafficking antiquities.
The sculpture of Hindu goddess Uma Parameshvari is thought to have been stolen from a Shiva temple in Tamil Nadu in southern India.
The decision to return the item came after discussions between Singapore's National Heritage Board and the Indian government body looking after its antiquities, the Archaeological Survey of India (ASI).
The ASI submitted an official request for the return of the sculpture in May, according to the museum.
"While there is no conclusive proof that the sculpture was stolen from a Shiva temple in Tamil Nadu, India, ACM took note of the confession of Aaron Freedman, who was the manager of Art of the Past, of dealing in looted Indian antiquities and of criminal possession of 150 stolen objects," the museum said in a statement.
It was one of 30 objects ACM bought from the art dealer, although none of the others are thought to be listed as stolen. The ASI was reportedly allowed to view them, anyway.
The museum said it will take legal action to get compensation for the apparent fraud.
A Singapore museum will return to India an 11th Century sculpture believed to have been stolen from that country.