The team also transferred right-hander Easton McGee to the 60-day injured list, also with a forearm strain.
Those moves allowed Seattle to make room for right-hander Bryan Woo, who was set to make his major league debut in Saturday's start against the host Texas Rangers.
Gonzales, 31, is 4-1 with a 5.22 ERA in 10 starts this season. He has 34 strikeouts and 18 walks in 50 innings.
Manager Scott Servais said on Friday that Gonzalez felt discomfort after throwing 5 2/3 innings last Sunday at home against Pittsburgh. The left-hander still wasn't feeling right when throwing his bullpen session earlier this week and remained in Seattle ahead of the team's weekend series at Texas.
McGee, 25, landed on the 15-day IL on April 30. He allowed on hit in 6 2/3 scoreless innings in his lone start of the season on April 29 at Toronto.
Woo, 23, is 3-2 with a 2.05 ERA in nine starts this season at Double-A Arkansas. He has struck out 59 batters and walked 12 in 44 innings.
Reuters and The Associated Press contributed to this report.