The injury occurred in Zurich on Monday, according to a US Soccer statement.
Dempsey has travelled back to Seattle for treatment and is expected to miss 2-3 weeks.
The former Fulham and Tottenham man will not be replaced in the squad for Wednesday's game against Denmark in Aarhus, leaving Jozy Altidore, Aron Johannsson and Rubio Rubin as Jurgen Klinsmann's options up front.
US Soccer could yet add a player for the game against Switzerland on March 31.
Dempsey has three goals and an assist from the Sounders' first two games of the new MLS season.
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