The Dutch international sustained a knee ligament injury in Tuesday's Champions League with former club Ajax.
Seedorf was forced off midway through the first half of the game at Amsterdam ArenA after a collision with Ajax defender Hatem Trabelsi.
The news is a blow for Milan's hopes of sustaining their bids in the Champions League and Serie A title race.
Milan have also received some good news on the injury front with Andrea Pirlo's knee problem not as serious as first feared.
The Italian international picked up a knee problem in training on Monday and it was feared he could face a lengthy spell on the sidelines.
Tests have shown there is no serious damage to Pirlo's knee and he should be fit again within 10 days.
