The Belgian star fractured his ankle during national team training on Sunday and will miss Monday’s friendly with the Czech Republic and Friday’s World Cup qualifier against Estonia.
Although no timeframe has been put on the injury, it is also a setback for his club.
Hazard, who joined Chelsea from Lille exactly five years ago for a reported £32million, was back to his best as the Blues won the Premier League under Antonio Conte.
Earlier in the day, he had said he would be happy to stay at Stamford Bridge – although he has not started talks about extending his stay.
Asked if he would like to see an offer, Hazard, who has three years left on his contract at Stamford Bridge, told the Het Laatste Nieuws newspaper: “Of course, that’s all.
“We all dream. It could be Spain, it could be staying with Chelsea.
“I think I can stay with Chelsea for many years, but it’s not something I’m thinking about right now. We’ll see.”
“‘We’ll see you after the vacation. Previously we talked about PSG (Paris Saint-Germain), now about (Real) Madrid, next year it will be a different club.
“In football you never know, but at the moment it’s not my mind. I’m a Chelsea player, I have another contract for three years. We’ll see.
“We had a great season with (Chelsea boss Antonio) Conte. We want to continue this season, now that we also play Champions League.
“We know it’s hard to conquer two titles in England, but we’re going to try it. It’s a pleasure to work with Conte.”
When asked if he had watched Real’s Champions League win against Juventus on Saturday night, Hazard added: “Yes, but if I ever wanted to go to Real, I could get there (and be) on the bench.
“I want the best solution for myself.”