At least 30 climbers were on the wall at the time, but it was not clear if the victims were climbers or tourists, ranger Scott Gediman said.
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"It was witnessed by a lot of people," he said.
The injured person was taken to a hospital near the park. No names were immediately released.
El Capitan is one of the world's largest granite monoliths towering 4,000 feet (1,219 meters) above Yosemite Valley.
Several people made emergency calls, reporting the rock fall from the Waterfall route on the east buttress of El Capitan.
Officials didn't provide details on the size of the rock fall, but climbers posted pictures on social media from hundreds of feet up the wall showing billowing white dust moments after the crash.
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Mountaineers from around the world travel to the park in the Sierra Nevada to scale El Capitan's sheer face. Fall is one of the peak seasons because the days are long and the weather is warm.
Ken Yager, president and founder of the Yosemite Climbing Association, reviewed photos of the cliff face and debris field, estimating the relatively thin piece that broke off covered an area big enough to fit five houses.
"It cratered and sent stuff mushrooming out in all directions," said Yager, fearing that its victim was someone he knew from the climbing community.
Rock falls are common in Yosemite but seldom fatal.
Climber Kevin Jorgeson said he and climbing partner Tommy Caldwell witnessed a massive rock fall in the same area while they prepared for a trek that made them the first people to free-climb the Dawn Wall on El Capitan in 2015.
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First they heard a rumble and then they saw a white cloud of dust.
"Yosemite is just a really active, wild place. It's always changing," Jorgeson said. "It doesn't make it any less tragic when someone gets in the way of that."
In 2013, a rock dislodged and severed the rope of a Montana climber who was scaling El Capitan.
Mason Robison, 38, fell about 230 feet to his death. It was Robison's gear digging into the side of the mountain that caused the rock to dislodge.
Yosemite remained open after Wednesday's rock fall, and other activities throughout the park weren't affected, rangers said.