Navarra Hospital Dr Manuel Montesino said three people sustained head injuries while another suffered an arm injury in the run.
A regional government said the four were Spaniards and none was in serious condition.
In the nationally televised morning runs, participants dash along with six bulls and accompanying steer down a narrow 850-metre course from a holding pen to Pamplona's bull ring.
Today's run lasted 2 minutes, 28 seconds.
The nine-day fiesta became world famous with Ernest Hemingway's 1926 novel "The Sun Also Rises" and is now one of Spain's most important tourist events.
Many people suffered falls and were trampled on by the beasts or other runners. In one incident, four bulls crashed into a bunch of participants close to the end of the race, and several people narrowly missed being gored.
Bull runs, or "encierros" as they are called in Spanish, are a traditional part of summer festivals across Spain. Dozens of people are injured each year in the runs, mostly in falls.
In all, 15 people have died from gorings in the San Fermin festival since record-keeping began in 1924.
The festival started yesterday with the traditional midday launching of a firework rocket - known as the "Chupinazo" - from Pamplona's town hall balcony.
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