The Netherlands international was taken off five minutes before half-time at the Stadio Olimpico, sparking fears the centre-back may need to go under the knife.
However, following scans on Monday, the Serie A club's worries over De Vrij's long-term fitness were eased.
Club doctor Stefano Lovati told Lazio Style Radio: "The ligaments are healthy and therefore he will not have to undergo any surgery.
"From today he will start therapy and follow a physiotherapy program. Obviously the boy will be monitored.
"When there is a sprain, the ligaments still feel the shock but in our case we are fortunate that they are not damaged."
Stefano Pioli has seen his side win eight league games on the bounce to move second in the top flight.
However, amid De Vrij's injury news, the Lazio coach also learned that a broken rib will sideline Marco Parolo for 20 days while Diego Novaretti will wear a protective hand cast to allow him to return to training later this week.
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