Steven Gerrard has confirmed Konsa will be out for between 12 to 16 weeks after suffering the injury in a challenge with Palace forward Jean-Philippe Mateta.
But the Villa boss expressed some relief the problem was not more serious, conceding he initially feared the 24-year-old might have sustained ligament damage.
Gerrard said: “It isn’t great news, but we’re quite relieved because we thought we were dealing with an ACL. Thankfully, it’s not that.
“He should return, all being well, at the back-end of August or the beginning of September.”
Goalkeeper Emi Martinez is, meanwhile, a doubt for tomorrow’s visit of Burnley after suffering a knock in training on Wednesday morning.
The Argentina international will be assessed ahead of the game with Roma loanee Robin Olsen on standby if required.
Leon Bailey and Kortney Hause both remain out and are not expected to feature again this season.