The Australia midfielder suffered the problem after a heavy fall during the first half of last weekend’s home victory against Ipswich.
Jedinak could be fit again in six weeks but if the 33-year-old needs surgery then his recovery time would be around three months.
“He went to see a specialist in Manchester on Monday. He’s been advised to rest and see how it is in the next week to see if it starts to heal itself,” Villa boss Steve Bruce told the club’s official website.
“If it does, we can let nature takes its course and it could be six weeks then. If it doesn’t, then there will be an operation which will probably take the best part of 12 weeks.
“We hope the specialist is right and rest is sufficient, then we could see him back in January.”
Jedinak’s is the latest significant injury problem to beset Bruce after captain John Terry suffered a broken foot and striker Jonathan Kodjia injured the ankle he broke in the final game of last season.