The Japanese defender was substituted after 76 minutes as Inter held rivals AC Milan to a 1-1 draw on Sunday.
Nagatomo, 26, is likely to miss both legs of the Europa League tie with Tottenham as well as several Serie A fixtures.
Following initial fears that Nagatomo would have to sit out the rest of the season, Inter announced that the injury was not serious enough to warrant surgery.
A club statement read: "The outcome of the tests carried out was that he has a capsular ligament injury to the external meniscus and minor damage to the external ligament."







