The bull-run, which lasted only around two minutes, saw Jandilla bulls tear through the streets of the Navarran city, hot on the heels of hundreds of runners in the annual tradition of the San Fermin Festival.
A 30-year-old British man was gored between the legs in the perineum area, the regional government of Navarra, of which Pamplona is the capital, said in a statement.
A 38-year-old from California was gored in his right armpit and another 27-year-old American was also gored in an undisclosed spot.
None of the injuries were considered to be life-threatening.
Eight other men, including three Americans, were treated in hospital for bruises and scrapes suffered in falls.
Runners, wearing traditional white clothing and red kerchiefs around their necks, tripped over each other or fell in the mad rush as they and the animals charged down a winding 846.6-metre (925-yard) course from a pen to the city's bull ring in two minutes, 23 seconds.
Some dared to run just at arm's length from the six huge bulls and six steers that accompany them, glancing nervously behind at the beasts' curved horns.
One black bull raced ahead of the pack and made several charges at the runners, who scrambled to get out of the way.
On Monday, a sea of revelers decked in red and white sprayed wine on each other in a packed Pamplona square to kick off Spain's famed fiesta once frequented by author Ernest Hemingway.
The nine-day street party got underway at midday with the cry "Viva San Fermin!" followed seconds later by the firing of a firecracker known locally as the "chupinazo".
Crowds wearing traditional white outfits trimmed with red neckerchiefs and cummerbunds drank from traditional leather wine pouches and sprayed red wine on others. Others poured wine from balconies overhead.
Five giant outdoors television screens were set up at other points in the city centre and aired the event live.
Pamplona is located just south of the Rioja vineyard region and wine has for centuries played an important role in the celebrations, which commemorate San Fermin, the city's first bishop and patron saint.
The festival, immortalised in Ernest Hemingway's 1926 novel "The Sun Also Rises", dates back to medieval times and features religious processions, folk dancing, concerts and round-the-clock drinking.
Just over six tonnes of fireworks will be set off during a nightly sound and light show during the festival which wraps up on
But the highlight is a daily race of courage pitting hundreds of people against a pack of six half-tonne fighting bulls charging along a winding, 846.6-metre (more than half a mile) course through narrow streets to the city's bull ring where the animals are killed in an afternoon bullfight.
The bravest run as close to the tips of the horns as possible without being gored.
The first bull run, which traditionally draws the largest number of participants, in . A run takes on average just under four minutes.
15 killed since 1911
Dozens of daredevils are hospitalized each year. Most of the injuries are not caused by bull horns but by runners falling, or being knocked over and trampled by the animals.
Fifteen people have been killed in the bull runs since modern day records started in 1911.
The most recent death took place in 2009 when a bull gored a 27-year-old Spaniard in the neck, heart and lungs.
A runner being knocked over during Tuesday's first bull-run. Photo: AFP
Last year just over 17,000 people joined the festival's eight daily bull runs with over half of them, 56 percent, coming from abroad, according to Pamplona city hall.
The United States, Australia, New Zealand and Britain accounted for the greatest number of foreigners. The vast majority of bull run participants are men.
The Navarra Hospitality Association forecast that hotel occupancy in the centre of Pamplona would average about 85 percent during the festival, about last year's level.
"It is a unique festival," the head of the association's data department, Jorge Fernandez, told AFP, adding that revelers came from the world over right from the United States to Australia.
Pamplona city officials refused to provide an estimate for the number of visitors expected in the city of 300,000 residents this year.
But they said just under 1.3 million people took part in 2014 in the over 400 events linked to the run.
The regional government of Navarra said 3,350 police would patrol the streets to keep the events as safe as possible.
About 100 semi-naked animal rights activists daubed themselves with fake blood and stood outside of Pamplona's bullring holding signs that read: "Pamplona's streets are stained will bull's blood" in several languages.