The Serbian striker was introduced as a substitute with 15 minutes remaining in Saturday's 3-1 win over Milan at Stadio Olimpico and unwittingly set up Marco Parolo for his second goal and Lazio's third.
However, in doing so Djordjevic fell awkwardly when he rolled his ankle on the ball and was subsequently taken from the field on a stretcher.
An X-ray assessed the extent of the damage and Lazio subsequently confirmed the severity of his injury in a statement on their official website, with the forward set to have an operation on Tuesday.
"Thank you all for your messages of affection," Djordjevic wrote on Twitter.
"I will address everything with grit and courage."
Djordjevic has scored seven goals in 20 Serie A appearances since making the move to Rome in the close-season.
