It happened around 1 a.m. near the intersection of Broad and Webster streets.
Police tell Action News the Uber driver was headed south on Broad when gunfire erupted on the street.
A bullet shattered a back window of the Uber and the 28-year-old passenger suffered a graze wound to the head.
The victim was rushed to the hospital in stable condition.
Police said they found numerous spent shell casings on the scene.
No arrests have been made.