The incident occurred Sunday night in Port St. Lucie in a hotel room that looked out on a pool where two teenage girls saw him, the report said.
Levis was released from the St. Lucie County Jail shortly after 1 p.m. on Tuesday on $50,000 bond.
"Obviously, we're looking into it," Red Sox spokesman John Blake said Tuesday. "We take these things very seriously and we won't have any further comment until we've had a chance to look into all the facts."
Port St. Lucie is the spring training home of the New York Mets.
The 39-year-old Levis is a pro scout who began working for the Red Sox in November 2006.
He spent parts of nine seasons, from 1992-99 and 2001, in the majors as a catcher with Cleveland and Milwaukee. In 319 games, he batted .255 with three homers and six RBIs.