Media reported that the 30-year-old could be out for the rest of the season.
Gattuso suffered the injury in Sunday's 1-0 Serie A win at home to Catania and had tests on Tuesday.
"They showed a tear to the anterior cruciate ligament of the right knee," a club statement said.
The tough-tackling midfielder will visit renowned knee surgeon Marc Martens in Antwerp early on Wednesday for a further consultation before a decision on whether to operate is taken.
Gattuso won the World Cup with Italy in 2006 and helped Milan clinch the 2004 Italian title and the Champions League in 2003 and 2007.
England midfielder David Beckham arrives at Milan in January for a three-month loan from Los Angeles Galaxy while Mathieu Flamini and Massimo Ambrosini could also fill in for Gattuso.
Milan are joint second in Serie A this term, six points behind leaders Inter Milan.
Italy top World Cup qualifying Group Eight and next visit Montenegro in March.
