Varlamov has been sidelined since Dec. 7, missing nine games, because of what the team is calling a lower-body injury.
He is 12-1-2 with a 2.21 GAA and .924 save percentage for the Southeast Division-leading Capitals.
The move to Hershey was announced Tuesday. Varlamov is expected to rejoin the Capitals next week.
The 21-year-old was selected for Russia's Olympic team last week.