University officials said the crime happened around 12:50 p.m. Wednesday at a residence in the 3200 block of Winter Street.
The unsuspecting victim was a 22-year-old Drexel student returning to her off-campus home. She was followed inside by a stranger.
The victim asked the suspect to leave and that's when he attacked, putting her in a headlock.
"He forced her upstairs to the second floor to a bedroom where he raped her," said Capt. Burgmann.
The female student described the suspect as: "A black male, 18-23 years old, 5'5" tall, with a round face. He has a soft voice and was wearing all black: black hooded sweatshirt, black pants, black shoes. He was wearing a rag or t-shirt on top of his head," said Capt. Burgmann.
Police issued a sketch of the suspect on Friday night.
Some students Action News spoke with said they are on edge by the crime.
"It freaks me out, to be honest. I don't like thinking about it. Like I live a little further up the block, like that could have been me, could be one of my roommates, could have been one of my friends," said senior Ioanna Tegos.
"I just wish someone was there for her that could have, you know, had her back at that moment, obviously she was in dire need," added senior Taylor Kent.
Some students said they immediately took precautions after receiving a notification from the university.
"I make sure that I have my dog with me if I'm walking around the area, my apartments, or even the city in general because you never know," said Kat Bottger.
"It's a lot of 'stay together' and 'being more alert of our surroundings' because we never really thought anything of it," added junior Reilly Swanson.
The suspect fled in an unknown direction and is still at large.
If you have any information contact the Special Victims Unit at 215-685-3251 or the Drexel University Police at 215-895-2222.