He is quarantined at home in Houston, where he received the result.
Oakland general manager David Forst said Thursday that Mengden was placed on the injured list. The A's added new left-hander Mike Minor to the 40-man roster after acquiring him Monday in a trade with the Rangers.
"He continues to be asymptomatic and feels good," Forst said while discussing Mengden on a conference call.
The team's three-game series at Seattle this week was postponed, as well as last Sunday's scheduled series finale at Houston, where the A's learned late Saturday of one positive test. Forst said the A's left Houston in two groups, the second being those who had close contact -- up to 15 minutes -- with Mengden in the 48-hour window during which he tested positive.
The A's don't know how Mengden contracted the coronavirus. There haven't been additional positive tests within the traveling party.
"There was no breaking of protocols," Forst said. "That's frankly what's scary about this virus."
The A's returned to the field at the Coliseum for workouts Wednesday with another session scheduled for Thursday as they prepare to host the Padres beginning Friday night after being cleared by Major League Baseball to resume their season on Thursday. Oakland faces playing three doubleheaders in a seven-day span starting next Tuesday.
The Associated Press contributed to this report.