Finch was playing for Yorkshire's Second XI's in their three-day match against Worcestershire's Second XI when he edged a pull shot into his ribs.
The Melbourne Renegades batsman was forced to retire hurt in his first red-ball match of the summer after he started spitting up blood.
Finch walked off the field unaided after the incident and was taken to hospital to have scans.
The medical results are expected to come through on Thursday after Finch wasn't required to stay in hospital.
Aaron Finch walks from the field after being struck in the ribs playing for Yorkskire (Photo from Twitter)