Walsh reported soreness in his foot at training on Friday and was sent off for scans, which revealed a hot spot.
Carlton say there is no fracture in the foot and surgery isn't required, but a period of recovery is needed to allow the injury to settle.
The Blues hope Walsh will return in either round 19 or 20.
That means he will not only miss Sunday's clash with West Coast in Perth, but also games against North Melbourne, Port Adelaide, Collingwood and Brisbane, before a possible return against Melbourne in round 19.
Carlton's season is already hanging in the balance at 5-7, and the loss of Walsh is a big blow to their hopes of clawing back into the top eight.
Jaxon Binns has been called up into Carlton's 23 to take on West Coast.
"It's more in the early stages which is why the timeline isn't as long as what it could've been," Carlton coach Michael Voss said of Walsh's injury on Saturday.
"We're fortunate enough we caught it early, but all these things always come with inconvenient timing.
"It's inconvenient for everyone, for him and for us.
"He's a real pro. Once he knows what he's dealing with, he turns his mind into his rehab, how he can get better and how to get the most out of the situation.
"He'll take his five or six weeks and hopefully we get him back better and stronger."
Carlton have already lost Nic Newman (knee), No.3 draft pick Jagga Smith (knee) and Brodie Kemp (achilles) for the rest of the season, while star forward Harry McKay will miss his second consecutive match due to knee soreness.
West Coast have made three changes from the team that lost to North Melbourne by 10 points last week.
Tom McCarthy, the No.1 pick from the mid-season rookie draft, has been named for his AFL debut, while Clay Hall and Bailey Williams return to the side.
Premiership defender Tom Cole will spend a stint on the sidelines with a hamstring injury, while Brady Hough (illness) and Archer Reid (omitted) are the other outs.
Meanwhile, All-Australian West Coast backman Jeremy McGovern faces an anxious wait after fronting the AFL's concussion panel on Thursday night.
McGovern hasn't played since being concussed in the round eight loss to Melbourne on May 3, and the concussion panel will decide whether he can continue his decorated 197-game career.
A decision on McGovern's future is expected within the next week.
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