"We have to accept that we're not in a position to retain the number of employees we had in pre-corona times," its chief executive Thomas Woldbye said.
The lay-off plan, which is subject to changes, would apply across all functions, the airport operator said.
If 650 jobs are cut, CPH estimates it would lead to annual cost savings of some 325 million Danish crowns ($52 million), although with only a limited effect in 2020.
CPH, the biggest airport in the Nordic region, said talks with union representatives would be held in the coming weeks to decide on the expected redundancies.
Separately, CPH reported a 55.5% drop in revenue for the first six months as a result of the coronavirus crisis.
The airport, which had close to 30.3 million passengers pass through its gates in 2019, said flow in the first half of 2020 was 65.2% lower than the same period last year, when the number was 14.4 million.
In June, the firm forecast a significant drop in annual revenue and said it expected an overall loss after tax in the range of 450-750 million crowns for 2020.
Shares in CPH were up 0.22% at 0742 GMT.
($1 = 6.3012 Danish crowns)
(Reporting by Nikolaj Skydsgaard, additional reporting by Tim Barsoe; Editing by Jason Neely and Alexander Smith)