Palace officials said the prince, who will turn 91 on Saturday, was taken to the King Edward VII Hospital in London from Windsor Castle on Monday as a precaution and will remain under observation for a few days.
As the Diamond Jubilee show ended, Prince Charles took the stage and encouraged concertgoers to make some noise for his father. The crowd responded with a roar and chants of "Philip."
The heir to the throne paid tribute to his mother, addressing her as "Your Majesty - Mummy" and leading the crowd in three cheers for the monarch.
Despite Philip's illness, many members of the royal family, including Charles, his wife Camilla, Duchess of Cornwall, and Princes William and Harry sat in a royal box to watch the show, performed on a specially erected stage outside the palace.
The queen was cheered as she arrived partway through the show, wearing a gold lame cocktail dress under a dark cape. It was decided before Philip's illness that she would watch only part of the concert.
The queen is not a noted pop music fan, and appeared to be wearing yellow ear plugs as she observed the concert.
Some 12,000 contest winners watched the show from an enclosed area, while a huge crowd stretched down the Mall, the wide boulevard leading up to the palace.
The lineup featured a full hand of knights - McCartney, John, Cliff Richard and Tom Jones, all "Sirs" - along with Dame Shirley Bassey and younger artists including JLS and Kylie Minogue.
The show opened in a blaze of sound and color, as a scarlet-clad military band joined Robbie Williams onstage for his hit "Let Me Entertain You." Black Eyed Peas star Will.i.am performed "I Gotta Feeling" with songstress Jessie J.
In true something-for-everyone mode, performances ranged from pianist Lang Lang playing Gershwin to American soprano Renee Fleming to 64-year-old Grace Jones hula-hooping her way through "Slave to the Rhythm."
Performers from around the world sang a special jubilee song written by Andrew Lloyd Webber and "Take That'''s Gary Barlow.
It was the veteran entertainers who went down best. The crowd roared along to Cliff Richard's "Congratulations," and cheered Bassey singing - fittingly - "Diamonds are Forever." Prince Harry could be seen singing along - "Why, why why?" - as Tom Jones belted out "Delilah," while Prince William and his wife Catherine joined in on John's "Crocodile Rock."
Ska band Madness performed 80s hit "Our House" on the palace roof, changing the lyrics to "Our house, in the middle of one's street."
The queen may not like to rock'n'roll but she has plenty of fans among rock's elite.
Before the show, Elton John paid tribute to the monarch's constancy.
"She's not trendy, she doesn't follow any fads," John told the BBC. "She's stoic, she's brilliant, she's wise, she's funny, and we're all really happy to be here."
McCartney closed the concert playing "Ob-La-Di, Ob-La-Da" on a Union Jack guitar before the queen took the stage with her family - but without Philip, who until Monday had been her constant companion throughout the jubilee celebrations.
He had joined the queen and senior royals on the River Thames in cold and blustery weather Sunday for a pageant in honor of Elizabeth's 60 years on the throne
The prince, who married then-Princess Elizabeth in 1947, has cut back on official engagements in recent years but still maintains a busy schedule. He spent four nights in the hospital over Christmas after suffering chest pains and underwent a successful coronary stent procedure to clear a blocked artery.
The palace said Philip was "understandably, disappointed about missing this evening's Diamond Jubilee Concert," as well as a St. Paul's Cathedral service and other jubilee events planned for Tuesday.
"I'm very sorry he's going to miss the concert because he's really part of the celebration," said Canadian tourist Marielle Demorsce. "He's part of the 60 years, he's put in a lot of work with the queen to appear all over the world and we love him too so very much."
The jubilee was being marked around the world in members of the 54-nation Commonwealth of former British colonies.
At the end of the concert, the queen lit the last in a chain of more than 4,200 commemorative beacons that have been set alight in Britain and abroad.
One beacon was lit in Kenya at the Treetops Hotel, where Elizabeth was informed of her father's death in 1952, making her the queen.
Although not everyone has embraced the jubilee - anti-monarchists have protested, and some 2 million Britons used the four-day holiday weekend to leave the country - many said it gave them a sense of pride.
"Sixty years on the throne is a remarkable achievement," said 47-year-old Dean Caston, who joined the crowds outside the palace on Monday. "People knock Britain and how depressed we are, but this weekend you can see we have got a lot to be proud of."
Associated Press Writer Robert Barr contributed to this report.