The Russian spacecraft carrying Russians Alexander Skvortsov and Oleg Artemyev and American Steve Swanson launched successfully into orbit from Kazakhstan on Tuesday night and was expected to reach the space station in six hours.
But Nasa said the arrival was delayed because an engine burn "did not occur as planned".
The US space agency said the crew was in good spirits and in no danger but will have to wait until today to arrive at the space station.
Russian spacecraft used to routinely travel two days to reach the orbiting laboratory before last year. All onboard systems were working flawlessly, Nasa said.
Roscosmos, Russia's space agency, said the glitch occurred because of a failure of the ship's orientation system.
The crew have taken off their space suits to prepare for the long flight and are working to adjust the spacecraft to the right orbit for today's docking.