Also on Wednesday, the Twins recalled both catcher Willians Astudillo and right-hander Sean Poppen, who is set to make his major league debut.
Gonzalez, 30, had been playing through hamstring discomfort, according to manager Rocco Baldelli, with the injury not expected to be serious. He was batting .255 for the Twins with nine home runs and 26 RBIs, but was hitting .309 since May 2 with seven of those home runs and 19 RBIs.
Parker, 34, whose family emergency was not disclosed, was 0-2 with a 4.26 ERA in 27 appearances and had nine saves.
Astudillo, 27, batted .250 with two home runs and 11 RBIs in 33 games with the Twins earlier this season. Poppen, 25, is a Harvard product who posted a combined 2.97 ERA in 13 games (11 starts) at the Double-A and Triple-A levels.
The Twins entered play Wednesday with an American League-best 48-24 record.
--Field Level Media