Wilmots' men looked to be heading to a comfortable win after goals from Marouane Fellaini and Radja Nainggolan put them in command, only for Max Gradel to equalise in injury time after Didier Drogba had pulled one back for the visitors.
Hazard replaced Kevin Mirallas in the 62nd minute, but was unable to make any real impact as he sustained the injury almost immediately after his introduction.
And the knock could come as a blow to Premier League leaders Chelsea, who face London rivals Tottenham on Saturday, but Wilmots refused to take any blame.
"His (Hazard's) sock was broken and his ankle was immediately quite swollen," Wilmots said.
"Such things happen in top-class football."
Belgium spurned a number of chances to kill off the game against Sabri Lamouchi's men, with Aston Villa's Christian Benteke firing over from close range with the goal at his mercy early in the second half.
But, despite letting a comfortable lead slip, Wilmots expressed satisfaction with his side's performance.
"In the second half, the rhythm was going down a little bit after I substituted some players," Wilmots added.
"We scored two goals, but I think that with (Christian) Benteke's chances we could have scored two more goals.
"But I can say that I very happy of what my players showed on the pitch."
