The first "encierro" or bull run on Sunday through Pamplona's old quarter left six people injured, including three who were gored, the Royal Navarre Hospital said in a statement.
A 23-year-old U.S. man and a 40-year-old Spanish man were both gored in the thigh, while two young Spanish men sustained head injuries.
A 46-year old man from San Francisco was gored in the neck in the city's bullring, at the end of the 850-meter (930-yard) course.
Toms Belzunegui, a spokesman with the regional hospital in Pamplona, says three runners have head injuries or severe bruises.
The centuries-previous bull run custom takes place every morning over eight days during San Fermin.
The festival was immortalised in American novelist Ernest Hemingway's 1926 book, "The Sun Also Rises".
People from around the world come to Pamplona every year to get chased by bulls.
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Handscomb, 28, has played 21 one-day internationals for Australia , with a century and four fifties to his name. There were also concerns the lingering fall-out from the ball-tampering scandal would prove a distraction.
This year, the bulls were from cattle breeder Puerto de San Lorenzo, whose bulls have been responsible for one goring incident in the past.
53 people were treated by the Red Cross during the Running of the Bulls festival in Spain and 5 were rushed to a hospital nearby after sustaining injuries that were caused by the charging bulls.
Bull fights and bull runs are a traditional part of summer festivals across Spain.
The local Red Cross said emergency personnel attended to 48 people with less serious or minor injuries, including two who were trampled by the racing bulls.
One person was gored on the opening day of the festival past year.
Each day during the fiesta, runners try and test their luck and skills at getting close to the stampeding wild bulls.