Spanish broadcaster RTVE reported that the 28-year-old was injured as a crush of fallen runners blocked the entrance to the bullring, briefly stopping the bulls from entering it.
The man was described as being in a "serious" condition with asphyxia caused by crush injuries to his chest.
Four other participants in the festival were taken to hospital for cuts and bruises, said Javier Sesma, health spokesman for the province of Navarra.
The event drew widespread attention on Friday when the American college student and two Spaniards were gored, and videos and photos of the attacks were seen around the world.
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