Naismith was injured during Sunday's 3-0 Betfred Cup semi-final defeat at the hands of Celtic at Murrayfield.
The Scotland international will return to parent club Norwich for a further scan, but Hearts boss Craig Levein says Naismith will need surgery and hinted he might not be available until around Christmas.
"It looks like he's got a little tear in his cartilage, which we suspected." Levein said, before adding of the potential absence: "Maybe six to eight weeks or something like that - but I'm guessing.
"We've had a number of blows in the last three or four weeks so we will just have to cope with this one as well as we have done with the other ones.
"It does leave us a bit thin on the ground up top with Uche (Ikpeazu) being out as well, but we'll get by."