Hazard managed 13 minutes against leicester last weekend and just over half an hour in the midweek Champions League win over Qarabag after returning from an ankle injury.
Chelsea host Arsenal on Sunday and manager Antonio Conte says the Belgian will feature, but Drinkwater will miss out and faces a spell on the sidelines.
The summer buy from the Foxes has a calf injury and Conte has confirmed the England international will have to wait until October before making his Chelsea debut.
Conte said: "He had a muscular problem in his calf. I think it's very difficult to see him before the international break. He needs time to recover.
"It's a pity because he was starting to work and to improve his physical condition.
"Now we have to move all these situations. And in two, three weeks, four weeks, I don't know."
Conte also confirmed Gary Cahill is likely to start after he missed last week's win at Leicester through suspension.
On Hazard and Cahill, he said: "For sure Eden is improving and is very close to being fully fit. I think he's improving a lot.
"Gary came back against Qarabag and played very well, a good performance. I am pleased for him. I have another day to reflect and then make the best decision for Sunday."