The versatile midfielder will not be fit for the Rossoneri's next fixture, but is expected to be back playing very soon
The Italy international picked up a knock in the San Siro side's 3-1 win over Bologna, and has since been working on his recovery.
"I am feeling much better now and can’t wait to get back. I am happy, because the injury is not as bad as it seemed at first," Montolivo stated to Milan Channel.
"Now we will evaluate the situation with the medical staff and decide the right moment to resume training with the full squad."
The former Fiorentina playmaker then went on to stress that Milan has an attack that's on par with the best front-lines in Serie A if everybody's fully fit.
"When all of our players are fit and available, our strike force will be on a par with any of the other Italian teams," he explained.
Milan is currently preparing for its league match at home against Atalanta on Saturday.