The Honolulu Museum of Art handed over the seven antiquities to personnel from the US Immigration and Customs Enforcement's (ICE) Homeland Security Investigations (HSI).
It was following a probe during which it emerged that the objects had been stolen from temples and ancient Buddhist sites in India and brought to the US illegally.
ICE agents will bring back the items here to be eventually returned to the Indian government. Authorities said the museum was not aware that the stone objects had been stolen when they were added to its collection between 1991 and 2003.
Homeland Security officials in Honolulu contacted the museum last year after special agents in New York determined that a 2,000-year-old terracotta rattle sourced from Kapoor's NYC gallery might have found its way into the museum's collection.
Subsequently, the museum, working in close collaboration with HSI, identified six other Indian artifacts, including figurines, architectural fragments and tiles in the institution's possession with potential ties to Kapoor, who was the subject of an Interpol Red Notice and was arrested in late 2011 in Germany.
He was extradited to India, where he is awaiting trial. The statues were seized as part of an HSI Cultural Property, Art and Antiquities Programme investigation titled 'Operation Hidden Idol'.
"Looting is a serious problem in the art market and all buyers of art, including museums, need to be mindful that some antiquities have been illegally obtained," Honolulu Museum of Art director Stephan Jost said.