The incident took place on the night of September 11 at the Sriji temple in Barsana, near Mathura.
According to the FIR, the woman was sleeping on the balcony of the temple when a watchman and another staffer forcibly took her to a secluded place and took turns to rape her.
Police have arrested the temple's watchman, Kanhaiya Yadav, while the other accused is on the run, SP (Rural) Aditya Kumar Shukla said.
He added the victim has been sent to a hospital for medical examination.
The woman told reporters that she approached police on the evening of September 13 but no FIR was registered.
The FIR was lodged on September 14 after the intervention of SSP Swapnil Mamgai.