The playmaker sustained the injury in training with Belgium on Sunday.
A tweet from his national team read : "Medical imaging showed that @hazardeden10 has a fracture in his right ankle #belcze #estbel #roadtorussia."
No timeframe has been put on the injury - although he will miss Belgium's international against the Czech Republic on Monday and a World Cup qualifying match in Estonia on Friday
However, it may impact on Chelsea - for whom Hazard was back to his best last season as they won the Premier League under Antonio Conte
The 2017/18 campaign starts in less than 10 weeks on August 12 - but three weeks before that there are pre-season games against Arsenal, Bayern Munich and Inter Milan in Singapore from July 22-29, then the Community Shield against the Gunners on August 6.
Earlier on Sunday the Hazard had said he would be happy to stay at Stamford Bridge - but admitted an approach from Real Madrid would be considered.
Asked if he would like to see an offer, the 26-year-old, 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.
''Previously we talked about PSG (Paris St 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 in my mind
I'm a Chelsea player, I have another contract for three years
We'll see."
Asked if he watched Real's Champions League win against Juventus, Hazard continued: ''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.''
On Chelsea's campaign, he added: ''We had a great season with 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.''
Source : PA
Source: PA