Another four people were hospitalised for other injuries picked up as runners tripped over each other and fell as they opened a path for the six half-tonne fighting bulls and six steers.
A 25-year-old Australian man, known only as JG, has undergone surgery after being gored three times by the same bull that gored another Australian.
That man, a 24-year-old from Grenfell in New South Wales, is reportedly doing well and is due to be released from hospital.
Festival spokeswoman Lucinda Poole says the older of the two men has injuries to his abdomen and his left thigh.
"He is being operated on in traumatology in the hospital complex and they say the condition is grave, which translated to English probably means extremely serious," Ms Poole said.
The Department of Foreign Affairs says it is providing consular assistance to the man.
A 595-kilogram bull named Olivito slipped and became separated from the pack turned around to face the runners and repeatedly charged one young man, lifting him in the air and pinning him against a wall.
It was not immediately clear which of the men was the one gored by Olivito.
The man managed to escape but the bull quickly caught up with him, goring him again as he tried desperately to pass to the other side of a wooden fence that separated runners from spectators.
A bull that separates from the pack presents one of the greatest dangers in the bull runs, leaving the huge animal disoriented and more likely to charge runners.
Monday's run was the longest of the eight in this year's festival and the bulls from the Miura ranch in Seville in southern Spain took four minutes and 47 seconds to tear along a winding 848-metre course from their holding pen to Pamplona's bull-ring.
In all, 42 people have been hospitalised after taking part in the bull runs this year, including seven for gorings.
The morning bull runs are the highlight of the nine-day festival which dates back to the Middle Ages and was immortalised in Ernest Hemingway's 1926 novel The Sun Also Rises.
Fifteen people have died from gorings since records started in 1911, most recently in 2009 when a 27-year-old Spanish man was gored in the neck, heart and lungs.