The six bulls and six steers charged 846.6 metres from a pen to the northern city of Pamplona's bullring in just two minutes 11 seconds, the swiftest since 1990, a festival spokeswoman said.
The heaviest bull, a light brown 635-kilo (1,400 pound) beast named "Resiston", broke away from the pack in the final stretch leading to the bullring and charged several runners.
It struck one daredevil in the back with its head before hooking him by the armpits with its horns and tossing him to the ground.
The bull then leapt over the man, who scrambled on his hands and knees to the side of the road.
The injured, aged from 20 to 56, suffered fractured bones, cuts and bruises but no gorings. They were all taken to hospital for treatment.
They included three Americans and a French citizen, organisers said. Among them, a 31-year-old from New York dislocated his shoulder and a 20-year-old from Chicago injured his chin and bruised his back in a fall.
"The bulls came too fast, almost nobody was expecting them to appear so quickly. I started to run on the right side and someone pushed me and I fell," said 27-year-old Jorge Montilla from Madrid.
Crowds from around the world lined the route.
Some stood on garbage bins or climbed electricity poles to get a better look.
About 165 emergency services workers and 16 ambulances were spread across the route.
Every year between 200 and 300 participants in the run are injured, around three percent seriously. Most are hurt after falling but some are trampled or gored by the bulls despite increased safety measures.
The last death occurred two years ago when a bull gored a 27-year-old Spaniard to death, piercing his neck, heart and lungs with its horns in front of hordes of tourists.
The bulls can reach speeds of 24 kilometres (15 miles) per hour and are particularly dangerous when they become separated from the pack.
Four men have been gored so far this year at the festival, including two during Tuesday's bull run.
A 40-year-old Pamplona man underwent a three hour operation on Tuesday after he suffered a 20-centimetre-deep goring that broke through his diaphram but missed his vital organs.
A 25-year-old Australian man was gored in his right thigh during Friday's bull run after he taunted one of the bulls and a 23-year-old French foreman was gored the following day, less seriously.
The final bull run will be held on Thursday, the last day of the San Fermin festival.
The city of some 200,000 residents expects the festival will at least match last year's turnout figure of 1.5 million people and a hotel occupancy rate of over 90 percent.