The discovery was made around 8:25 a.m. Saturday in the 5300 block of Chestnut Street.
That's where officers found the victim, a woman in her early 30s, in the passenger seat of a gold Honda Odyssey.
The victim had multiple stab wounds to her body and one in the face, police say.
She was pronounced dead at the scene.
Philadelphia police said Saturday night that person of interest was in custody. He was only identified as a 34-year-old man.
The name of the victim has not been released.