"To be honest it's going to be very tough, but I have to wait and see how the operation goes," the Barcelona centre back told a news conference on Wednesday when asked whether he would be fit for the tournament.
"But I think it's impossible because when you come out of an operation there is a recovery period and I believe that those who are in better shape should go," added the 34-year-old.
The loss of the talismanic Puyol, who is hugely respected by team mates and opponents alike, is a significant setback for the world and European champions, who begin the defence of their continental title against Italy on June 10.
His absence will likely mean that coach Vicente del Bosque will deploy Real Madrid's Sergio Ramos alongside Barca's Gerard Pique in central defence, with Javi Martinez of Athletic Bilbao another option.
"It's one of the worst pieces of news we could have expected but we have to deal with it and find solutions, although it won't be easy," Del Bosque was quoted as saying in As sports daily.
"Puyi is a titan and his absence means Spain is losing part of its soul," added the former Real Madrid coach, who is due to announce his final squad on May 27.
"We are talking about a player who is an example on and off the pitch and is key in both matches and at training camps."
Barca announced on Tuesday that Puyol had sustained an injury to his right knee that required arthroscopic surgery and would sideline him for around six weeks.
The shaggy-haired centre back damaged the knee in last weekend's La Liga match at home to Espanyol and is due to have the operation on Saturday.
He will be unavailable for the King's Cup final against Athletic Bilbao on May 25, the club said.
Puyol, one of the team captains, has been a reliable presence in the Spanish back line for more than a decade, making 99 appearances and scoring the winning goal in the 1-0 semi-final victory over Germany at the 2010 World Cup.
"I am not saying I am retiring or not retiring from the national team," Puyol told reporters at Wednesday's news conference.
"Right now the operation is the important thing and later we'll see. It's not only my decision," he added.
Spain also face Ireland and Croatia in Group C at the tournament in Poland and Ukraine.