Birmingham Fire Batallion Chief C.W. Mardis says the worker was getting onto a platform outside the building Thursday when his safety equipment malfunctioned.
Mardis says the worker's safety gear slowed his descent somewhat, and he was fortunate to land in an area with newly planted bushes and mulch, which might have broken his fall.
Mardis says the worker was conscious when he was taken to UAB Hospital, where he's recovering.
Doug Ecker of Hoar Construction says the worker is affiliated with an Atlanta construction firm.
Children's of Alabama spokeswoman Rachel Olis says the 14-story building has been under construction but is nearing completion and is scheduled to open this summer.