The star posted a photo of him greeting Aiden, a patient at the Savannah hospital's Pediatric Specialty Ward.
Some scenes of the Baywatch reboot were filmed at the hospital.
"Awesome experience and THANK YOU to all the hard working and caring staff who helped make this visit possible. To all the kids I met - you guys keep smiling and staying strong. All the mamas and daddy's I met, y'all stay strong too," Johnson wrote.
"Gotta tell ya little stuff like this will always be the best part of fame. And good Lord I wish I had Aiden's concentration when I was in my high school math classes. I wouldn't have failed Algebra twice."
Earlier this month, Johnson confirmed that David Hasselhoff will be in the Baywatch movie, which also stars Zac Efron, Alexandra Daddario, Kelly Rohrbach and Priyanka Chopra.
Baywatch hasn't got an official release date yet but, according to a follow-up Instagram post from Johnson, it looks set to be released in May 2017.