The visit is part of events marking the centenary of diplomatic relations between both countries.
Prince Frederik and President Duda are expected to deliver addresses during a ceremonial breakfast.
In the afternoon Prince Frederik and Duda will attend energy talks between Danish and Polish experts related to the construction of the Baltic Pipe gas line and Poland's planned green energy cooperation with Denmark.
The Danish guests are also expected to lay flowers at Warsaw's Tomb of the Unknown Soldier and open a conference devoted to Polish-Danish relations at Warsaw University.
The programme of the visit also includes a joint meeting of the Polish presidential couple and the royal Danish couple with Polish and Danish veterans of foreign missions, which will take place at Warsaw's Centre of Foreign Missions Veterans.
Prince Frederik and his wife are also scheduled to attend the unveiling of a plaque commemorating Danish sculptor Bertel Thorvaldsen, the creator of Warsaw's memorials to astronomer Nicolaus Copernicus and Prince Jozef Poniatowski.
In the late afternoon the Danish royal couple will attend a gala concert commemorating the 100th anniversary of Polish-Danish diplomatic relations. (PAP)