Wainwright was injured while batting Saturday night in Milwaukee. He is scheduled for an MRI exam Monday.
"Whether it's strained or torn … I don't think it's good news," General Manager John Mozeliak told the St. Louis Post-Dispatch on Sunday.
"I don't like to speculate until you have the full information, but if you ask me how I feel ... not good. All those rumors floating around seem to have some validity to them."
Several published reports said the Cardinals expect Wainwright to be out for the season. Manager Mike Matheny would say only that the pitcher will be examined when the team returns to St. Louis.
Wainwright, 33, was put on the 15-day disabled list. He is 2-1 with a 1.44 earned-run average in four starts this season.
The three-time All-Star is 121-67 for St. Louis, and was their star closer in 2006 when they won the World Series.
Washington Nationals ace Max Scherzer probably will be scratched from his next scheduled start, Tuesday at Atlanta, because of a sprained right thumb.
The right-hander threw off flat ground before Sunday's game at Miami but said his thumb is still sore. He jammed it batting Thursday against St. Louis.
"We'll probably have to make an adjustment on Tuesday," Manager Matt Williams said. "I don't anticipate him missing more than one turn, but again you don't know."
Williams said he didn't know who would replace Scherzer against the Braves.
Scherzer, the winner of the American League Cy Young Award in 2013 with Detroit, is 1-2 with a 1.26 ERA in four starts.