The baby boy was allegedly “assaulted” at a playground in Sheldon, Birmingham.
A 36-year-old man is also being treated in hospital and has been arrested on suspicion of assault.
West Midlands Police has launched a major investigation into the incident, Birmingham Live reports.
A full statement from the force read: “Officers were alerted by ambulance colleagues to reports that a baby had been hit in the eye with a golf ball on a playground outside Radley court on Sheldon Heath Road, just after 8:40pm last night (June 28).
“The three-month-old baby boy was taken to hospital with a serious eye injury, where he remains this morning.
“A 36-year-old man was arrested on suspicion of assault and is currently in hospital.
“An investigation is underway and anyone with information is asked to contact police via Live Chat at www.west-midlands.pnn.police.uk between 8am and midnight or call 101 anytime.
“Please quote crime reference number 20BE/153313J/19.
“Crimestoppers can be contacted anonymously on 0800 555 111.”
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