Wheaton is expected to be sidelined for four to six weeks, the Chicago Sun-Times reported, citing league sources.
Although Wheaton was listed as limited in Thursday's practice and was not on the team's injury report Wednesday, the newspaper reported that he was awaiting final results of an MRI exam.
The 26-year-old Wheaton has appeared in only three games with Chicago, making his lone reception for nine yards in Monday night's 20-17 loss to the Minnesota Vikings.
Signed to a two-year, $11 million contract in March, Wheaton has had a rocky first season with the Bears. He underwent an emergency appendectomy during the first week of training camp and broke a finger on his left hand in August.
His injury is the latest blow to a receiving corps that lost Cam Meredith to a torn ACL during a preseason game and former first-round draft pick Kevin White to a fractured collarbone in the season opener.
Wheaton spent his first four NFL seasons with the Pittsburgh Steelers, hauling in 97 of his 108 career receptions during the 2014 and 2015 seasons.