Park spokeswoman Kari Cobb says Aleh Kalman has been missing since witnesses reported seeing him get pulled to the edge of 594-foot Nevada Fall on Saturday afternoon.
A search team assisted by a California Highway Patrol helicopter spent the rest of the day unsuccessfully looking for him, suspended the search when it got dark and then picked it up again on Sunday morning.
Cobb says the river's current was moving very quickly, with a temperature in the low 50's, when Kalman disappeared. He was visiting Yosemite with a church group.
Officials have closed the trail below the falls while the search continues.