Poland's largest lender did not provide reasons for the resignation, which takes effect on Feb. 14.
Since his appointment in April last year, Szwed has been the fourth chief executive officer after the long-reigning Zbigniew Jagiello left the bank he had led for 12 years.
Poland's new government is seeking changes on the boards of state-controlled firms after winning elections last year.
Last week a general meeting of shareholders at PKO BP voted to replace members of the bank's supervisory board, with the State Treasury using its shareholder rights to appoint Katarzyna Zimnicka-Jankowska as chairwoman.
Similar changes have taken place on the boards of state-owned refiner Orlen, the largest company on the Warsaw Stock Exchange, as well as at other utilities in which the government holds stakes.
The shares in the bank moved little on the news, losing 0.5% at 1019 GMT.
(Reporting by Mateusz Rabiega; editing by Jason Neely and David Evans)
By Mateusz Rabiega
