The 26-year-old is expected to be sidelined for a number of weeks after picking up the problem during training with Belgium over the weekend.
It is not clear how long Hazard will be out of action for but there have been suggestions that the playmaker could face a race to be fit for the start of the season with Chelsea.
Azpilicueta was quick to pay tribute to Hazard after learning about his club team-mate’s injury and wished him all the best in his recovery.
Hazard played a key role in helping Chelsea win the Premier League title under Antonio Conte last season, scoring 16 goals in the top flight.
Apzilicueta was also a regular fixture in the Blues’ starting line-up, as he played every single minute of Chelsea’s Premier League campaign.