It's reported that Sir Alex kicked a football boot in the dressing room at Old Trafford that flew and hit Becks above the eye.
It happened after United lost 2-0 to Arsenal in the fifth round of the FA Cup on Saturday.
Sir Alex told Granada television said: "Things like that happen in the dressing room.
"It was one of those freak accidents of nature that happens and then it's over."
Earlier in the day Beckham didn't look very happy when he left his house to go to training and a plaster could be seen above his left eye.
No one is suggesting that Sir Alex meant to hurt the England captain.