The incident happened at around 8.20am this morning and involved two airport vehicles.
A spokesman for Edinburgh Airport said: "We can confirm that two airport vehicles were involved in a collision whilst attending a possible bird strike on an aircraft.
"As a result our runway was closed for a short period of time and has now reopened.
"An investigation is now underway."
A British Airways flight travelling from London Gatwick to the airport was diverted to Glasgow as a result of the collision.