Jamar injured his posterior cruciate ligament during Melbourne’s 96-point win over Adelaide Crows at the MCG on Sunday.
Although four to six weeks has been estimated, there is a possibility Jamar could return earlier, based on further assessment on Wednesday.
The 27-year-old said he was aiming to return as soon as possible.
“I’m disappointed not to be out there playing,” Jamar told melbournefc.com.au.
“I’m doing everything possible in my recovery to get back out there as soon as possible to help the boys out on the field.”
The 2010 All-Australian has continued his fine form this season, combining strongly with midfielder Brent Moloney.
Jamar has played 101 matches, having notched up the ton against West Coast Eagles in round six.