The Yugoslavian international was stretchered from the field during the first half of the Roman club`s 2-1 win over Bari on Friday night.
Lazio official Felice Pulici said: "He has had the operation on his cruciate ligament and we will see how things go."
Stankovic had earlier voiced his displeasure at failing to command a regular starting place at the Stadio Olimpico and this is unlikely to have lightened his mood.
The injury is also a blow to the under pressure England manager-elect, who has seen his side struggle in the defence of their Serie A crown, as well as falter in the Champions League, meaning there have been calls for the club to sever ties with the Swede.
However, Lazio and Eriksson have stood firm and stated that they will both honour the remainder of the contract, which runs out at the end of the season, and they will be hoping for a bright start to the New Year.
