With Sunday's contest 1-1 on the hour mark, Aidoo attempted to kick the ball before it went out of play, but the defender lost his balance and fell backwards.
As he landed at Zidane's feet and knocked the coach over, the player's legs went up and his left boot caught the Frenchman on the left cheek.
The two made sure each was OK before Aidoo ran back onto the pitch to rejoin the action.
Zidane twice touched his face straight after the collision, before telling reporters after the game that he is "fine."
"Yes, he hit me but anyway, I have to be there [on the touchline]," Zidane added.
The incident comes days after Zidane was involved in a car accident last Saturday on his way to training.