The 90-year-old prince was taken to the King Edward VII Hospital as a precautionary measure. He was expected to remain hospitalized under observation for a few days, the palace said.
Despite Philip's illness, members of the royal family including Prince Charles, his wife Camilla, Duchess of Cornwall, and Princes William and Harry sat in a royal box to watch the concert, featuring performances by Paul McCartney, Elton John and Stevie Wonder.
"I hope he's OK," said McCartney, who was due to close the concert. "We all send our best wishes for a speedy recovery."
The queen was cheered as she arrived partway through the show, wearing a gold lame cocktail dress under a dark cape. Some 18,000 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.
Until Monday, Philip had been the queen's constant companion throughout the jubilee celebrations. On Sunday, Prince Philip joined the queen and senior royals on the River Thames in cold and blustery weather for a pageant in honor of Elizabeth's 60 years on the throne.
Philip, who is also known as the Duke of Edinburgh, is a former naval officer who married the queen in 1947. His health remained robust through his 80s, but he has appeared frailer in recent years. He has cut back on official duties, but he still carries out engagements, both with his wife and on his own.
The Associated Press contributed to this report.