The American, aged 46, was in a serious condition after being gored in the neck, said a medical report from the Navarra regional authorities.
Another American, aged 23, and a Spaniard were also hospitalised after being gored during the bull run, one of the most crowded events of the week-long San Fermin festival. Both men were gored in the left thigh but their condition was not as serious.
Another three people, all Spaniards and aged between 18 and 38, were also hurt during the run.
The Red Cross in Spain had warned that the event would be especially dangerous because of the large number of people.
On each morning of the festival, at eight o'clock, six bulls are released from a corral to run through the narrow, cobbled streets of the old town.
Hundreds of people dressed in white shirts and red scarfs, try to run ahead of bulls to the city's bull ring, where the animals are killed by matadors in afternoon bullfights.
Sunday's run was a relatively fast one, the bulls taking just two minutes and 41 seconds to cover the 848 metres (925 yards) through Pamplona's narrow streets to the bull ring.
The week-long festival, which also involves religious processions, concerts and all-night drinking, attracts thousands of visitors from around the world.
Bull fights and bull runs are a traditional part of summer festivals across Spain.
Anyone over the age of 18 can take part in the Pamplona runs though authorities warn of the risks. Since 1911, 16 people have been killed in the event. The last death was in 2009.
The San Fermin festival and the running of the bulls was immortalised in Ernest Hemingway's 1926 novel “The Sun Also Rises”.