The injuries had initially been described as life-threatening.
The incident occurred in the top of the second inning when Oakland infielder Brett Lawrie's bat shattered during contact with a pitch and flew into the stands.
A police spokeswoman told the Globe that a female fan seated with her husband and son in the second row of stands along the third base line was struck in the head by a shard of the bat.
ESPNBoston.com reported the woman was "bleeding pretty profusely," and that a nearby fan offered his shirt to medics for their use. A small child nearby was "shaken up" and shielded from the scene by a law enforcement officer, according to the Globe.
The victim could be heard screaming as she was removed from the stadium on a gurney, WEEI radio reported.
Police said the woman, who was not identified, was taken to a local hospital, according to the Globe.
Scary situation in Boston: Game halted as fan was injured after being struck by a shard from Brett Lawrie's bat, rushed off by medics.— 120 Sports (@120Sports) June 5, 2015
A policeman was holding a young child and shielding his or her eyes. Fans in the area trying to help. Lots of blood. Awful scene.— Pete Abraham (@PeteAbe) June 5, 2015
It looks like fan who left game had a child with her. Child was carried out by medics while she shrieked in pain. Brutal to see and hear.— John Tomase (@jtomase) June 5, 2015
A shard from Brett Lawrie's broken bat struck fan sitting in third-base boxes. Bleeding pretty profusely. Other fan offers shirt to medics— Gordon Edes (@GordonEdes) June 5, 2015