US Soccer said that both Dempsey and Johnson had to withdraw from the squad and no replacements would be added.
Dempsey strained his right calf during training Wednesday morning in Glasgow.
Johnson is still troubled by a nagging right ankle injury.
USA faces Scotland on Friday at Hampden Park in Glasgow and four days later take on Austria for the first time since 1998.
Star striker Landon Donovan as well as Clarence Goodson, Edgar Castillo and Brad Guzan are also battling injuries and were not in coach Jurgen Klinsmann's squad.
The United States qualified for their seventh consecutive World Cup and won the six-team North American qualifying competition.
Revised USA squad
Goalkeepers: Bill Hamid (D.C. United), Tim Howard (Everton), Sean Johnson (Chicago Fire)
Defenders: DaMarcus Beasley (Puebla), John Brooks (Hertha Berlin), Geoff Cameron (Stoke City), Brad Evans (Seattle Sounders FC), Omar Gonzalez (LA Galaxy), Eric Lichaj (Nottingham Forest), Michael Orozco (Puebla)
Midfielders: Alejandro Bedoya (Nantes), Michael Bradley (Roma), Mix Diskerud (Rosenborg), Jermaine Jones (Schalke), Sacha Kljestan (Anderlecht), Brek Shea (Stoke City)
Forwards: Jozy Altidore (Sunderland), Terrence Boyd (Rapid Vienna), Aron Johannsson (AZ Alkmaar), Eddie Johnson (Seattle Sounders FC), Chris Wondolowski (San Jose Earthquakes)