The Belgium international sustained the problem in last weekend's 2-2 draw at Wigan but it was not picked up until 48 hours later.
His injury was scanned while he was in Belgium and the results were sent back to the club's Finch Farm training ground for Everton's medical staff to assess.
Fellaini was withdrawn from World Cup qualifiers against Serbia and Scotland and will return to Merseyside on Monday for treatment.
"I am currently suffering from a knee injury: fortunately it is not too serious but I will have to miss the two games with Belgium," he told evertonfc.com.
"I am hoping to be back playing for Everton as soon as possible.
"I am extremely disappointed and I now have to rest in order to get back to full fitness so I can help the team with some important games coming up."
Everton travel to bottom club QPR a week on Saturday before hosting Liverpool in the Merseyside derby the following weekend.