The crash happened around 9:11 p.m. at the intersection of B and Venango streets.
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Investigators say the driver of a dark-colored minivan with logos on the side went around a stopped vehicle on B Street and struck the pedestrians.
The driver of the minivan then fled the scene, continuing southbound on B Street.
A 56-year-old woman was taken to Temple University Hospital in critical condition with head trauma and internal injuries.
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Two other victims, a 59-year-old man and a 32-year-old man, suffered wrist injuries and were last reported to be hospitalized in stable condition.
"To strike one person in a hit-and-run is unconscionable, but to strike three people and just keep going - it's exceptionally callous," said Capt. Robert Heinzeroth of the Philadelphia Police Department's Crash Investigation Division.
Anyone with information is asked to contact investigators at (215) 685-3180.