The moves comes a day after Morton allowed three runs on three hits with four walks and three strikeouts in 4 2/3 innings of a 4-3 loss to the Athletics.
Morton is 13-3 with a 3.14 ERA this season.
He is the second Astros starter to go on the disabled list this month. Lance McCullers Jr. has been out since Aug. 5 with a forearm injury.
The Astros have not named a replacement for Morton, who was due to start Saturday against the Angels.