Manchester United's Diogo Dalot, on loan to AC Milan, has replaced the Manchester City right-back in the Portuguese squad with the titleholders opening their Group F campaign against Hungary in Budapest on Tuesday.
Cancelo's exit represents a blow to coach Fernando Santos coming just 48 hours before Cristiano Ronaldo's 2016 Euro winners take on the Hungarians.
They the face Germany in Munich four days later with world champions France waiting for them back in Budapest on June 23.
Cancelo is now self-isolating after Saturday's test result.
"According to the Covid-19 protocol established by UEFA before Euro 2020 matches every player in the squad underwent RT-PCR tests on Saturday. The results, with the exception of Joao Cancelo, were negative," the Portuguese federation announced.
Cancelo is one of a number of Euro players to contract coronavirus.
Russia's build-up to the delayed European Championship was hit when winger Andrei Mostovoy tested positive and was ruled out on Friday, the day before their opening game against Belgium.
And Spain skipper Sergio Busquets is self-isolating and out of their opening game against Sweden on Monday in Seville after testing positive last weekend, two days after a warm-up match against Portugal.
Sweden forward Dejan Kulusevski of Juventus and midfielder Mattias Svanberg also tested positive, with six reserve players called up on stand-by.
