"After tests we conclude he is unfit to participate in the World Cup," it said. Nani picked up the injury in training on Friday in Lisbon before flying to South Africa.
GEAR:Check out Portugal's WC kits
The winger had missed the squad's final home training session in Portugal on Saturday after falling while attempting an acrobatic shot and causing a traumatism in his shoulder.
During the flight to Johannesburg, he had been confident he would recover in time.
Nani's loss will be sorely felt by the 2006 semi-finalists who lost to runners-up France in Germany.
The winger had an excellent second half to the season with impressive performances in the Premier League and Champions League with Manchester United.
He will be replaced by Benfica's Ruben Amorim, the Federation added.
The other main injury concern in the Portuguese squad is Pepe, who has been recovering from a knee injury he sustained in December.
He has not played since but was last week cleared by doctors from the national side and his club Real Madrid to travel to the finals.
Portugal play their first tournament match on June 15 against the Ivory Coast in Group G, which also includes Brazil and North Korea.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
