Scans on Friday confirmed the latest setback for the unlucky 27-year-old, who has managed just 19 of a possible 45 senior games since the start of 2020.
The Blues will know the full extent of the injury once McGovern undergoes further assessment next week.
"It's a bit of a loss," Blues coach Michael Voss said.
"We'd like some more positive news and we were hoping to get him up and going for next week but we've lost him for a little while."
In better news for Carlton, key forward Harry McKay has been cleared to play against North Melbourne on Saturday night despite lingering knee soreness.
Boom recruit George Hewett is only expected to miss one match with a calf issue and will be replaced by debutant Jack Carroll at Marvel Stadium.
The smooth-moving left-footer, who was selected with pick 41 in the 2020 draft, has impressed over the last fortnight after overcoming some minor injury concerns.
Carroll will slot into the midfield alongside captain Patrick Cripps, Adam Cerra and Matthew Kennedy, who returns after one week out with soreness.
"(Carroll) is tough, he's hard and I know he'll do really well," Voss said.
"He works extremely hard and that always puts you in a really good starting point.
"He's worked really close with our mids right throughout pre-season and he's certainly mixed it with some of the bigger boys in there.
"He won't shirk a contest this young man. I think the Carlton faithful will be pretty happy watching his career unfold."
Voss backed inexperienced tall Tom De Koning to take on Kangaroos veteran Todd Goldstein, with Carlton's No.1 ruckman Marc Pittonet sidelined with a knee injury.
De Koning will be supported by defender Lewis Young and the versatile Jack Silvagni, who returns after overcoming an ankle sprain.
18°C