The Tynecastle skipper was injured following an aerial challenge with Johnny Russell just 19 minutes into the game at Tannadice on Saturday and had to be stretchered off the park after landing awkwardly.
A scan revealed that Zaliukas has completely torn one ligament and badly damaged another, so he now faces a minimum of eight weeks on the sidelines. He was already suspended for next month’s League Cup final against St Mirren.
“He got a scan yesterday afternoon and it was bad news,” McGlynn told Hearts TV.
“He’s torn a ligament completely and the other ligament is hanging by a thread basically, according to Rob Marshall our physiotherapist. We have to wait for a specialist now to see what the next stage is.
“He’s going to be out for a couple of months at least.”
Darren Barr and Dylan McGowan are the likeliest contenders to step in at centre-back, although Danny Wilson could also move in one, with Kevin McHattie restored at left-back. Zaliukas’ injury means McGlynn is now without three of his first-choice back four from the start of the season with Ryan McGowan having left in January and Danny Grainger absent since November with a serious knee injury.
Callum Paterson is out for the rest of the season after undergoing foot surgery, while Ryan Stevenson is banned for the next three matches, further decreasing McGlynn’s options.