Witnesses told Sky News the Royal Air Force Merlin helicopter was about 100 feet over a seaside hotel in Salthill when a side door gave way and fell on the crowd.
The injured were taken nearby University College Hospital and are said to be in a stable condition, Sky News reported.
Liam McBurney said he had been on top of the hotel taking pictures of the event when he saw about 100 people flee from the shoreline.
"The door fell off and was just like a piece of paper floating in the wind," McBurney told Sky News. "It floated over the promenade and crashed into the beach before bouncing about five to 10 feet into the air and landing again."
Although the airshow had ended, many of the spectators were milling about when the door hit the ground, he added.
A Ministry of Defense spokeswoman apologized for the incident and promised there would be an investigation into what happened, Sky News said.