The terminal of the airport can be seen flooded with water as people wait at the check-in desk for more information about their flights.
Heavy downpours caused widespread problems across the county on Sunday.
The airport said it was working to restore normal operations "as soon as possible".
In a statement, the airport said: "Following heavy rain today (Sunday 17 September) Exeter Airport has had to close due to flooding affecting the terminal.
“We are working to restore normal operations as soon as possible.”