The Belgium international has been blighted by ankle and leg problems since joining Zinedine Zidane's Spanish giants from Chelsea 18 months ago.
It was not immediately clear what his latest problem was, with Hazard able to walk off the Alfredo Di Stefano stadium pitch, albeit in obvious discomfort, to be replaced by Rodrygo after 28 minutes of the game.
Hazard had gone down in the Alaves penalty area moments earlier, although it was ruled that no foul was committed.
He was seen to grimace, stooping over after getting back to his feet and appearing to be in pain.
Last season he started just 14 games in the Spanish top flight, playing just a minor role as Madrid won the LaLiga title in his first season at the club.