Suarez was 2/3 with a 6.33 ERA in six starts for Triple-A Sacramento before making his season debut against the Braves. The 26-year-old missed 16 games while with the River Cats with a hamstring injury.
Suarez pitched against Atlanta twice in 2018 and beat the Braves on May 6 for his only career win.
Infielder Donovan Solano was optioned to Sacramento, leaving the Giants without a true backup shortstop. Manager Bruce Bochy indicated that third baseman Evan Longoria or second baseman Joe Panik could be used there if needed.
San Francisco also acquired minor league pitcher Matt Seelinger from Tampa Bay as the player to be named later in the deal that sent catcher Erik Kratz to the Rays last week. Seelinger will report to Class A Augusta.