West Midlands Police said they were called to a playground outside Radley Court in Sheldon Heath Road at around 8.40pm.
“Officers were alerted by ambulance colleagues to reports that a baby had been hit in the eye with a golf ball,” the force said in a statement.
“The three-month-old baby boy was taken to hospital with a serious eye injury, where he remains.
“A 36-year-old man was arrested on suspicion of assault.”
The suspect was also taken to hospital, according to police.
He is not believed to be related to the injured baby.
“An investigation is underway and anyone with information is asked to contact police,” the force added.
Witnesses are asked to call officers on 101 or Crimestoppers on 0800 555 111.