The hospital said two of the goring victims were Americans. One was identified as a 23-year-old man from Kentucky and the other as a 46-year-old man from San Francisco. The third victim was identified as a 40-year-old man from La Rioja in northern Spain.
Three others suffered injuries ranging from mild to serious, according to the hospital.
The centuries-old bull run tradition takes place each morning over eight days during San Fermin.
Traditionally, it was used as a way of getting the bulls from the city outskirts to the bull ring.