A Boston police spokesman said Bird is being "guarded by the Boston police at a local hospital" for evaluation. The spokesman said the victim had been taken to a different hospital due to the injuries.
Bird, 24, is expected to appear in court Monday, where he will face charges of assault and battery, strangulation and kidnapping.
The Celtics acknowledged in a statement that they were "aware of the incident" involving Bird and are "taking it very seriously."
The Celtics drafted Bird with the 56th pick in the 2017 draft. The shooting guard spent his rookie season on a two-way contract before being signed to the active roster this summer.
ESPN's Chris Forsberg contributed to this report.