Real Madrid's last training session ahead of the Champions League game in Ukraine did not feature Hazard or Carvajal as they completed individual training to recover from their injuries.
Gareth Bale, Dani Ceballos and Isco also missed the session as they are out injured.
All the international players are now back with the group under Carlo Ancelotti. Militao and Alaba recovered in time and will be available to play against Shakhtar Donetsk in Kiev.
Casemiro, Camavinga and Jovic were also able to complete the training session with the rest of the group, despite missing Saturday's practice.
After the training session, Real Madrid announced the squad to face Shakhtar and Hazard will stay in Madrid.