Are there nonstop flights from Mahón (MAH) to Barcelona (BCN)?

Yes. Ryanair, Vueling fly this route. Flight time is about 47m.

What is the fastest connection from Mahón (MAH) to Barcelona (BCN)?

via Palma de Mallorca ≈ 1h 23m, via Ibiza ≈ 1h 38m, via Valencia ≈ 1h 50m (estimated flying time, excluding layovers).

from 12,000 JAL miles (economy, one way, based on the published award charts).

Menorca Airport (MAH) to Josep Tarradellas Barcelona-El Prat Airport (BCN)・241 km

Nonstop flights available (2 airlines). Flight time about 47m. Nonstop return flights also operate.

With milesJAL 12,000 miles+ (via VLC)Economy, one way, estimate. Tap a connection for miles by cabin.

5 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.