The winger missed Saturday's victory over Stoke City with a calf problem, but was included in Belgium's international squad for the impending international break regardless.
However, Red Devils boss Roberto Martinez has now confirmed Hazard will miss a World Cup qualifier with Greece and the friendly with Russia.
Antonio Conte's side host Crystal Palace on April 1 before facing City at Stamford Bridge on April 5, and 26-year-old Hazard may now face a race to be fit for both games.
Martinez said: "Eden has suffered an injury before the match against Stoke, it does not look so serious.
"But he will not play against Greece. We are going to follow the injury.
"It is a big disappointment for Eden that he cannot lead the team. If you want to be a good team, you have to absorb everything.
"This is a good test for us. I see enough players who can take over his role."
Hazard has been in superb form this season, scoring 11 goals in 26 Premier League appearances for the west Londoners.
Conte named a front three of Willian, Diego Costa and Pedro against Stoke and would be likely to adopt a similar approach if Hazard is indeed ruled out of further fixtures as the Blues attempt to win their fifth top-flight title of the modern era.