The bus was carrying five band members and the driver, but police said Nelson was not aboard, KXAN-TV, Austin, Texas, reported.
The injured band members were taken to a hospital in Sulphur Springs.
Billy Jean English and Thomas Ray Hawkins received minor injuries but Robert Paul English suffered a broken hip.
The bus was traveling westbound on Interstate 10 when it hit a bridge pillar about 3:30 a.m., officials said. The pillar was not seriously damaged.
Officers with the Department of Public Safety said the roads were wet and winds were high at the time of the crash.
A message on Nelson's Facebook page said icy conditions contributed to the accident.
The message also said Nelson's tour had been suspended indefinitely.