The girl's mother filed a compliant at the Pernem police station on Tuesday evening, Jan 26.
Police inspector Uttam Rautdessai said, "The girl was bathing in the sea when a person started abusing her. The girl started crying and rushed to her mother, who was on a beach bed."
He further said, "She told her that the man, who we suspect is a tourist named Aman, had inserted his finger inside her."
The girl was later sent for medical examination to a government hospital in Panaji, which confirmed penetration.
The accused fled the scene when the girl complained to her mother.
Crimes against foreigners, especially Russians, have increased in Goa.
Earlier, a 25-year-old Russian woman was raped by a Goan politician in Dec 2009.