The LA Galaxy man will not be replaced on the roster, which now stands at 25 players.
Zardes, who is usually an attacker but has been playing an experimental right-back role of late, suffered the injury in the first half of Saturday night’s 1-1 draw against Real Salt Lake.
The U.S. faces Panama on Friday in Orlando, followed by a trip to take on Trinidad & Tobago four days later to conclude CONCACAF World Cup qualifying.
Full U.S. roster:
GOALKEEPERS (3): Brad Guzan (Atlanta United), Tim Howard (Colorado Rapids), Nick Rimando (Real Salt Lake)
DEFENDERS (9): DaMarcus Beasley (Houston Dynamo), Matt Besler (Sporting Kansas City), Geoff Cameron (Stoke City/ENG), Omar Gonzalez (Pachuca/MEX), Michael Orozco (Club Tijuana/MEX), Tim Ream (Fulham/ENG), Jorge Villafana (Santos Laguna), DeAndre Yedlin (Newcastle United), Graham Zusi (Sporting Kansas City)
MIDFIELDERS (9): Kellyn Acosta (FC Dallas), Juan Agudelo (New England Revolution), Paul Arriola (D.C. United), Alejandro Bedoya (Philadelphia Union), Michael Bradley (Toronto FC/CAN), Benny Feilhaber (Sporting Kansas City), Dax McCarty (Chicago Fire), Darlington Nagbe (Portland Timbers), Christian Pulisic (Borussia Dortmund/GER)
FORWARDS (4): Jozy Altidore (Toronto FC/CAN), Clint Dempsey (Seattle Sounders), Chris Wondolowski (San Jose Earthquakes), Bobby Wood (Hamburg/GER)
