The Danish gateway primarily attributes the upturn to growth on long-haul flights to Asia. Doha in Qatar, for example, makes its Top 10 most popular routes for the first time.
A total of 1.97 million travellers came through the terminals in the first month of the year.
"The growing demand for long-haul flights is a particular driver for the growth in traveller numbers," says airport CEO, Thomas Woldbye.
"The number of passengers on one of January's 36 long-haul routes increased by 13.6%.
"Quite a large proportion of travel to Asia now goes via the big hubs in the Middle East. Since Qatar Airways went from 14 to a typical 18 weekly departures in late summer, the traffic to and from Doha has increased - compared to January last year a 32% growth with 42,000 travellers."
Growth on the long-haul routes impacts the number of transfer passengers who fly into Copenhagen on the short routes, before flying on directly to the rest of the world. Transfer passenger growth was 6.3%.
"If we look behind the numbers, we can see that the transfer growth is particularly driven by the routes to China, India, and the USA – not least the SAS route to Hong Kong," notes Woldbye.
"To this should be added passengers flying into CPH and on to one of the big hubs in the Middle East."
SAS carries 80% of the transfer traffic in Copenhagen, while airlines such as Air Canada, Air China, Air India and Qatar Airways also contribute to the transfer traffic increase.
Domestic traffic fell by 6.2% in January, to 114,415 passengers. One of the reasons is that airlines offer 3.7% fewer departures.