The club captain, who missed last season's Champions League final through suspension, appeared to severely twist his ankle after a collision with Villa's Nathan Baker midway through the second half.
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"Maybe we paid too much - John Terry twisted his ankle, we're waiting for the scan to see how serious it is," interim manager Rafael Benitez told Sky Sports after the game.
"Hazard also felt something in his hamstring so again we're waiting for the scan. A pity for the final but at least we won and it was a good game."
The severity of both injuries remains to be seen, but with only four days until the Europa League final Chelsea will be hoping the PFA Young Player of the Year nominee, in particular, will not be sidelined for the foreseeable.