Both players started for Inter in Sunday's 3-0 victory at Napoli. However, defender De Vrij was substituted early in the game, while midfielder Dumfries limped off the field towards the end of the match.
The club did not provide a timescale for their recovery, but Sky Sports Italia reported that both players were expected to be sidelined for around 20 days.
Inter face Real Sociedad in their final Champions League group stage clash on December 12th, with top spot still up for grabs.