The new technology is part of the airport's ongoing investment in passenger-friendly check-in systems.
Finnair's new system will mean that passengers no longer need to queue up to check in for flights and can even proceed straight to security checkpoints if they have only hand luggage.
Henrik Peter Jorgensen, chief operations officer at the airport, said: "There is no doubt that mobile-phone check-in will be the check-in method of the future as it gives passengers a quick and flexible start on their journey.
"We are in ongoing and close contact with the other airlines in order to roll out the modern technologies, and we expect that it is just a matter of time before other airlines are also linked up to the mobile-phone check-in system."
Copenhagen Airport's collection of shops recently received a makeover with the addition of more seating and natural lighting.
More shops and restaurants are also expected to open during the next few months.