Costa is banned after being sent off in last weekend's FA Cup quarter-final defeat by Everton.
Hazard, who missed the game at Everton with a thigh problem, is again sidelined for the Premier League fixture with fifth-placed West Ham and has also been left out of Belgium's squad for the March 29 friendly against Portugal.
"Eden has discomfort in a tendon in the muscle from his upper thigh," Chelsea's interim coach Guus Hiddink told reporters on Friday.
"It will be good for him to rest. When he starts in the Euro (2016 finals in June) it will be with better physical fitness."
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With Radamel Falcao, Loic Remy and Alexandre Pato working their way back to full fitness, Hiddink has challenged his three back-up strikers to prove they are worthy of selection.
"Falcao has had a very difficult time with injury," said the Dutchman. "He has recovered... he has been training for 10 days with the first team.
"When we signed Pato (in January) we had a very difficult situation, the only competitive striker we had was Costa. We had Remy in troubled water.
"Falcao also, we have to see after the international break if he is fully competitive. We have to wait how he reacts to the more intensive training he is undergoing," added Hiddink.
"Everyone is getting fitter, that is the law of competition."
With Chelsea also out of the Champions League and languishing in 10th place in the Premier League, their season is effectively over and Hiddink said some of the less experienced players could feature over the final weeks of the campaign.
"There are chances that younger players can get their opportunity but ... they need to knock on the door," he added.
(Writing by Tony Jimenez,; Editing by Pritha Sarkar)
