"I can't even imagine the frustration that he's feeling and the emotion that he's feeling right now."
Wedge said the 35-year-old Gonzalez, who was unavailable for comment, would go back on the disabled list.
To make room initially on their 25-man roster for Gonzalez, the Indians designated outfielder Ryan Ludwick for assignment.
The injury to Gonzalez won't change Ludwick's situation, as Ludwick is not eligible to return to the Indians' roster immediately. The Indians have 10 days to trade, release or outright Ludwick, who's spent most of the past season rehabbing a knee injury, to the Minors.
Gonzalez's latest setback came after the Indians had trumpeted his return. General manager Mark Shapiro had announced earlier in the day that Gonzalez had been activated.
Shapiro said he was looking for Gonzalez's potent bat to add punch to the team's lineup, which is why Wedge had slid Gonzalez into the cleanup spot in the series opener against the Twins.
Wedge and Shapiro had described the 35-year-old Gonzalez, a two-time AL MVP, as a proven run producer, although they weren't counting on overusing him straightaway.
"We look at the guy right now, as we're phasing him back in, as three-to-four-day-a-week guy," Shapiro said of Gonzalez. "It'll be safe to say that he'll be in there against all left-handed pitching.
"He'll probably play more than that as well, as he demonstrates both the ability to contribute and to be healthy and strong. He could play more, but it'll be a gradual process."
On March 31, the Indians had put Gonzalez, who had signed with the Tribe in the offseason as a free agent, on the disabled list with a strained right hamstring. His injury occurred just days before the Indians broke camp in Winter Haven, Fla.
He remained in extended Spring Training and rehabbed the hamstring. On May 23, Gonzalez was sent on a rehab assignment in Triple-A Buffalo, where he batted .286 (6-for-21) with a run scored and an RBI in five games.
He played well enough there that he convinced the Indians he was ready to go full bore in the Majors.
But Gonzalez, who played for the Tribe in 2001, had not appeared in a Major League game since May 21, 2004, with the Royals. A lifetime .295 hitter, he's hit 434 homers and driven in 1,404 runs in 1,688 games.
Ludwick, 26, appeared in 19 games for the Tribe this season. He hit .220 (9-for-41) with four homers and five RBIs.
"Every decision we make with our roster is a tough one right now," Shapiro said. "This one was a tough one personally, because we all liked Ryan a lot.
"It's as much of a timing issue. You can't control the timing of injuries. ... To be the player he can be, he needs to play everyday right now. Hopefully someone'll give him an opportunity to do that, or he'll do that in Buffalo."