The 23-year-old midfielder -- signed from Bundesliga outfit Mainz for a reported £25 million in the close season -- has a right thigh injury which prevented him from playing in last Friday's 2-0 defeat by Aston Villa.
"Everton Football Club can confirm that Jean-Philippe Gbamin has sustained a tendon injury in his right quadriceps muscle, which will keep the midfielder out of action for at least eight weeks," Everton said in a statement.
"The full timescale for the injury will be established following further investigations this week," Everton added.
"The club are in communication with leading experts around Europe to ensure the optimal outcome."
Gbamin -- who represented France at every age level including Under-21 before opting to play for his country of birth -- signed a five-year contract with Everton on August 2, filling the void left by Idrissa Gueye's move to French champions Paris Saint-Germain.
Gbamin began his career at French outfit Lens before joining Mainz in 2016, where he made 86 league appearances and scored three goals.