The three runners, a 20-year-old American and two Spaniards aged 31 and 42, were all raced to hospital.
The extent of their injuries, the first gorings of this year's festival, was not immediately known, a Navarra hospital spokesman said.
Another three people, including a 48-year-old American, were taken to hospital with injuries suffered in falls during the sixth bull run of the hugely popular festival.
The run turned dangerous when a half-tonne black bull, part of the galloping herd of six sharp-horned bulls and six steers, separated and began charging into runners.
Two others then grabbed the young man by the feet and pulled him to safety.
An isolated bull is considered a more dangerous beast because it can become disoriented and is more likely to charge runners.
"A lot of people fell along the route, it was really dangerous," said Alan Carpenter, a 38-year-old banker from Chicago after taking part in his third Pamplona bull run.
The six bulls from the El Pilar ranch in the province of Salamanca completed the course in four minutes and 57 seconds, the slowest bull-fun so far this year.
The animals, which weigh between 510 and 575 kilos, will be killed by matadors in an afternoon bullfight.
The early morning bull runs are the highlight of the San Fermin festival, which was immortalised in Ernest Hemingway's 1926 novel "The Sun Also Rises" and now draws hundreds of thousands of tourists.
The most recent death took place four years ago when a bull gored a 27-year-old Spaniard in the neck, heart and lungs.
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