The midfield pair started the game at Stadio Marc'Antonio Bentegodi but captain Montolivo was taken off early in the second half while De Jong was withdrawn 12 minutes from time.
The Serie A club confirmed on Monday that they had picked up hamstring and thigh injuries respectively and would be reassessed in the near future.
"Both Riccardo Montolivo and Nigel de Jong sustained injuries during Saturday’s match away to Chievo," read a statement from Milan.
"Montolivo picked up a hamstring injury and he will undergo further medical tests in a week's time. Nigel de Jong meanwhile sustained a muscle injury in the back of his thigh. His fitness will be re-assessed in around 10 days' time."
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