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.

Jacob McIntyre's body was recovered from the River Ericht at Cally Bridge, near Blairgowrie, at about 12:35 on Sunday.
He had been reported missing from a property in the nearby Milton of Drimmie area at 11:15.
A police investigation into the circumstances of his death is continuing.
Police, firefighters, a water rescue unit and air ambulance were involved in the search.
Police Scotland said Jacob's family were "understandably upset at their tragic loss" and did not want to make any further statement at this time.
Det Chf Insp Iain Wales said: "This is a very tragic incident which resulted in a young boy sadly losing his life.
"The events will undoubtedly bring shock and sadness to this small community and further afield.
"We would like to thank our Scottish Fire and Rescue Service colleagues for their courage and assistance in Sunday's difficult conditions.
"Our thoughts and deepest condolences are with Jacob's family at this difficult time."
A Singapore museum will return to India an 11th Century sculpture believed to have been stolen from that country.
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A two-year-old boy found dead in a river after being reported missing in Perthshire has been named by police.