"Results of the breathalyser tests confirmed that four of the five crew members ... were above the legal alcohol limit of 0.2 promille," Romerike police prosecutor Edith Ek Sorensen told AFP.
The pilot, co-pilot and two stewardesses -- all from Latvia and employed by Air Baltic -- were taken into police custody and escorted to hospital for blood tests to confirm the breathalyser tests.
Results were expected later.
Sorensen said police had acted after receiving a tipoff from an anonymous caller around 4:00 am (0200 GMT).
The four risk up to two years in prison if found guilty.
Sorensen would not comment on the flight's destination, but Norwegian daily Dagbladet said it was a tour group flight operated by the Norwegian group Startour headed for Chania, Greece, with 109 passengers on board.