The 32-year-old Williams driver was penalised for impeding Bottas through Turns 6 and 7 during the first phase of qualifying.
"The team failed to inform the driver of Car 55 about Car 77 closing in on a flying lap and the driver did not take any action to make way for the incoming car," the FIA said in a statement. "The Stewards determine that Car 55 unnecessarily impeded Car 77."
The penalty drops Sainz to 20th on the grid and moves fellow Spaniard Fernando Alonso of Aston Martin, Cadillac's Sergio Perez and Bottas up one place each for Sunday's 57-lap race, the first Formula 1 grand prix to be held at the Madring.
Sainz, a former Ferrari driver and four-time race winner, has endured a frustrating campaign and lies 16th in the drivers' championship with six points. Williams are ninth in the 11-team constructors' standings.
Formula 1 champion Lando Norris secured pole position for McLaren with a superb final lap at the Madring, beating Mercedes championship leader Kimi Antonelli by 0.011 seconds.