Airport management surely needs to be done by people who understand what goes on at airports. I've come across engineers, firemen, pilots and air-trafficers who have progressed to that role- there's not a set route. Most didn't have an MSc or MBA so that may not be particularly necessary, but there's no good reason NOT to go that route if airport management is your career aspiration.
The best MSc deliverer in the English speaking world is Cranfield - and if they will have you, have a suitable course available, and you can afford the fees - I'd be amazed if you ever regret going there.
A very different organisation, but also offering a lot of really excellent packages is Embry Riddle Aeronautical University (ERAU) in the USA, who are globally well respected and I'm sure will do something similar.
Don't be afraid however to look wider at the broader management degrees - either an MBA, or an MSc in Air Transport Management (Cranfield or City would be obvious places for both of these for example).
One caution however - whatever academic qualifications you have, and they'll certainly be useful - there's no substitute for having significant relevant experience. Without that, you aren't employable at any senior level.
G