The 20-year-old was hurt during the first half of the League Cup semi-final against Inverness and failed to reappear for the second half at Easter Road.
Now a scan has now shown a hairline fracture within the knee, and doctors have told Smith rest is the best cure.
Hearts are still battling to escape administration and Locke's paper-thin squad is already without long-term casualties Jason Holt and Jamie Walker.
Locke told the club's website: "It's a massive blow for the lad as I thought he had being doing fantastic for us recently.
"The problem flared up after some gym work and we sent him for a scan (on Tuesday). He doesn't require any surgery and just has to rest then things should settle down.
"We are looking at around four to six weeks, though, which is a big blow at this stage of the season."