There is no airport in Monemvasia. The closest airport is located in Athens, the capital of Greece. The airport of Athens operates domestic flights from most Greek airports and also many international flights.
To go from Athens to Monemvasia, you can go by rental car or bus (via Sparti or Molai). You get the bus to Monemvasia from Kifissos KTEL Bus Station in Athens. The bus trip is about 5 and a half hours.