It happened just after 3:30 p.m. at 10th and Market streets.
Investigators say the attacker was captured on surveillance video as he got into an argument with the 67-year-old woman.
He then stabbed the victim multiple times and fled the scene on a bicycle, according to police.
The victim was transported to Jefferson University Hospital with stab wounds to her chest and back.
She's currently in the ICU with critical injuries.
"According to witnesses and at least one camera, you can see the perpetrator get on a red bicycle and drive off eastbound on Market from 10th," said Philadelphia Police Chief Inspector Scott Small.
Police say the suspect was wearing a gray hooded sweatshirt and the bicycle had a large bag attached to it.
Authorities believe the bicycle may be used to make deliveries.
Detectives are still trying to contact business owners to see if the crime or suspect was captured on any more surveillance cameras in the area.
"Preliminary information is the 67-year-old female and the perpetrator did know each other. We have a name now, so we believe we know who we are looking for," said Small.
Officers did not say what sparked the argument between the suspect and victim.
Anyone with information is asked to call Philadelphia police at 215-686-TIPS (8477).