The Spanish Red Cross said no one was gored in the hair-raising run but many runners could be seen slipping and falling on top of each other on the wet, cobblestone route. Some were trampled on by the half-ton beasts.
A Navarra regional government statement said a 48-year-old man from New York was treated for light head injuries, as was a 46-year-old man from Paisley, Scotland.
It said five Spaniards were also treated in city hospitals for minor injuries sustained the race.
Dozens of people are injured each year in the "encierros," as the runs are called in Spanish, most of them in falls. Fifteen people have died from gorings since record-keeping began in 1924.
Four Spaniards and an American have been gored so far in this year's festival but only one, a Spaniard, was said to be in serious condition.
The runs are the highlight of the nine-day street-partying festival, which was immortalised in Ernest Hemingway's 1926 novel "The Sun Also Rises." The festival attracts tens of thousands of foreign tourists.