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The striker sustained the knee problem in last Friday's 1-0 defeat at Sheffield United and Reds' boss Phil Parkinson said he was expecting to be without the 28-year-old for 'a significant period'.
After Smith saw a specialist on Tuesday, the bad news was confirmed.
"Unfortunately for Sam, he's done his cruciate and he's going to be out for nine months. He faces the operation next Wednesday," said Parkinson.
It leaves top scorer Kieffer Moore as the only fit senior striker, with 21-year-old Bailey Cadamarteri now set to get more game-time, but Wrexham are also without three attacking midfielders with Callum O'Hare joining Josh Windass and Nathan Broadhead on the sidelines.
Despite the absentees - wing-back Libby Cacace is also missing and is yet to play this season - Parkinson refuses to use injuries as an excuse and he won't let his side feel sorry for themselves.
"Callum O'Hare had to walk off the training pitch on Thursday before we went to Sheffield United and I just kind of started to feel, are we a team feeling sorry for ourselves?" he added.
"We can't be that team. We've had injuries in other years, we've had setbacks and we've always dug deep.
"I felt at Sheffield United, we looked like a team who've almost taken one blow too many, but I'm not accepting that.
"I think I've got to speak about injuries because you've almost got to make sure people are aware that the quality we're missing, but not use it as an excuse."