The 35-year-old did not return after half-time of Saturday’s 1-0 win over Hibernian at Parkhead after clashing with former Celt Efe Ambrose in the first half.
Gordon missed two years with a knee injury prior to signing for Celtic, but Rodgers allayed fears that the ‘keeper had injured the same knee.
“It’s sad news for him and for us but of course we will need to have that cover for someone to come in and support Dorus de Vries so that is something that we are looking at,” the Celtic manager said.
“It is Craig’s other knee as opposed to the one that had been injured and gave him problems.
“The medical staff had a look at him at half-time and there was that instability in the knee so it was just unfortunate.
“He is a great professional and while we are saying 12 weeks we are hoping he will be back sooner than that and all being well he will be.
“Dorus will come in and play. Has been a very loyal number two and settled into the club and has been very good in recent performances. He is calm and assured and experienced.”