Two BA pilots have been questioned by police about the incident on Friday.
The BA2945 flight to Gatwick, carrying 149 people, was delayed after the incident at 1930BST.
BA apologised and said: “We are investigating the matter and speaking to the pilots to understand the exact circumstances around the incident.”
The incident apparently followed the discovery of an unclaimed mobile phone on board.
The captain and co-pilot have been questioned by Lothian and Borders police, who are still investigating the incident.
A police spokesman said: “We are investigating after a mobile phone was reported to have been thrown from a plane on to the runway at Edinburgh Airport about 7.30pm on 24 June.”
A British Airways spokeswoman said: “We apologise to customers on the BA2945 from Edinburgh to Gatwick for the delay to the aircraft’s departure.
“There was a local airshow in aid of Armed Forces Day that meant some aircraft couldn’t depart or arrive for some time.
“This was further exacerbated as an unclaimed mobile phone was located on board so the aircraft returned to stand.”