The Irish airline has published the government minister's email address - which was already publicly available - on a website called 'Air Traffic Control Ruined Your Flight'.
A total of 5,782 Ryanair flights were affected by delays caused by Britain's air traffic control (ATC) provider Nats from the start of 2025 to September 1, the airline has said.
Ryanair has urged Alexander to "fix" Nats, which it has branded as "mismanaged and short-staffed".
The airline's director of communications Jade Kirwan said: "It is unacceptable that Nats' ATC mismanagement and staff shortages continue to cause disruption to UK flights and passengers.
"Already this year, more than one million Ryanair passengers - many of whom were travelling on holidays with their young families - have suffered unnecessary and avoidable ATC delays, and all because Minister Alexander has not taken action to properly staff UK ATC services.
"Ryanair calls on all passengers to visit the Air Traffic Control Ruined Your Flight webpage and demand that their national transport minister - like Minister Alexander - take urgent action to fix their national ATC services and stop these needless ATC delays."
The site also contains a mocked-up video of European Commission president Ursula von der Leyen slapping an airline passenger across the face.
Ryanair has also accused von der Leyen of failing to take action to improve ATC services across the continent.
Nats have declined to comment on Ryanair's actions.