His spokesman, Blazej Spychalski, said on Twitter that the 48-year-old conservative leader had received the result after taking a test on Friday.
He said the president feels well.
Mr Duda’s diagnosis comes amid a huge surge in the number of confirmed cases of Covid-19 and deaths in Poland, a nation that saw only very low numbers in the spring.
The spiking infection rates are pushing the country’s strained health system to the breaking point.
Doctors say patients are now dying not only from Covid-19, but from other illnesses that overwhelmed hospitals are not able to treat at the moment.
The government is preparing to open field hospitals, but it is not sure where it will find the doctors and nurses to staff them.
On Friday, Mr Dudda visited the National Stadium in Warsaw, which is being transformed into one of the field hospitals.
He also met Iga Swiatek, the 19-year-old Polish tennis player who won the French Open earlier this month.
Ms Swiatek said she and others on her team have no symptoms but would go into quarantine. She said they are tested regularly and would be tested again in three days.
The Polish government imposed new restrictions on Saturday that are just short of a lockdown in hopes of bringing the country’s outbreak under control.
Prime minister Mateusz Morawiecki appealed to Poles to strictly observe these “serious restrictions” in order to protect lives.
The appeal came as the nation of 38 million hit another daily record of new infections, more than 13,600, with 153 new deaths.
Overall, Poland has recorded 4,172 virus-related deaths during the pandemic.
Mr Duda’s key constitutional roles include guiding foreign policy and signing legislation.
But most of the day-to-day governance is the responsibility of Mr Morawiecki and his cabinet.