The full-back, 25, was hurt in Town's 3-1 defeat by Millwall on 9 April  - his first game since last December - and a scan has shown he needs surgery to repair ligaments.
"It's disappointing - he's just got back into the side," assistant boss Mike Jackson told BBC Radio Shropshire.
"Hopefully he'll get it sorted and be back playing as quickly as he can."
Demetriou, who is out of contract in the summer, has made 50 appearances for Shrewsbury, scoring three goals, since joining from Kidderminster Harriers in June 2014.
He spent the first half of this season on loan at Cambridge United and returned to the Shrews in January.
Following last season's automatic promotion, Shrewsbury are trying to avoid an immediate return to League Two over their final six games.
One point clear of the relegation zone, Town have a tough-looking start to their run-in with back-to-back home games against fourth-placed Bradford City and Sheffield United before trips to Gillingham, in sixth, and automatic-promotion chasers Walsall.
Micky Mellon's side then finish with two games against mid-table sides - Peterborough, currently 14th and Swindon in 16th.
Shrewsbury Town defender Mickey Demetriou will miss the rest of the season because of a knee injury.