Ryanair flight FR3532, which left Glasgow at 13:23 on Tuesday, landed safely and the pair were removed and detained by local police.
The aircraft then continued its journey to the Canary Islands.
A Ryanair spokesman said it would not tolerate unruly behaviour, and that passenger safety was a priority.
A flight from Glasgow Airport to Lanzarote was diverted to Faro, Portugal, after two passengers became "disruptive".