The winger suffered the problem during a training session ahead of the Premier League encounter with Stoke City and missed the 2-1 victory.
He travelled to Belgium on Monday as head coach Roberto Martinez was hopeful the attacker could play a role for the national team, but the 26-year-old is now due to return to Chelsea for further treatment.
"Eden's absence is obviously a big blow, but it will be interesting to see how we deal with it," Martinez said at a news conference.
"Eden suffered a calf injury the day before the game against Stoke. It does not appear to be too bad based on the information Chelsea gave us. Eden came to Belgium on Monday, but he will not remain with the group.
"Of course, this will be a disappointment for him. He is a very professional captain. But injuries are part of the game. A big test awaits without Eden."
Belgium top Group H with 12 points from four games, two points clear of Greece.