Described by Spain coach Vicente del Bosque as "part of the team's soul", Puyol had arthroscopic surgery on the knee to remove a detached fragment of cartilage and would likely be released from hospital on Sunday, doctors Ramon Cugat and Ricard Pruna told a news conference at Barca's Nou Camp stadium.
"Common sense dictates that he can't go to the European Championship," Cugat said.
"Why? Because he is injured and he underwent surgery today," he added.
"I am not the one to decide, but it is common sense that he can't make it. What he has to do is take care and make it back for next season."
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 in Poland.
His absence will likely mean that Del Bosque deploys Real Madrid's Sergio Ramos alongside Barca's Gerard Pique in central defence, with Javi Martinez of Athletic Bilbao another option.
Pruna was also asked about Barca's France defender Eric Abidal, who had a liver transplant last month and said the player would probably be allowed to leave hospital next week.
"A bit more than a month ago he had a transplant," Pruna added.
"The transplant went well. Slow but well. The player is doing well and will probably be given medical clearance next week. So we are happy about the process."