After a vigil sponsored by the group on Monday night, about 50 people broke away to march towards the police station.
Police then issued an alert on Twitter advising university residents to "shelter in place" due to "violent protests on campus".
Students told local media that police responded with tear gas after fireworks were thrown at them.
Three protesters were arrested, but officers did not immediately confirm if they were students at the Georgia Institute of Technology where the fourth-year engineering student was killed outside a dormitory late on Saturday night.
Schultz's mother noted that the engineering student was very active on campus
Video of the incident captured by a bystander shows Schultz saying "Shoot me!" several times while walking towards the officers.
"Drop the knife, man, come on," a police officer responds.
"Nobody wants to hurt you," another says, before one officer eventually opens fire, hitting Schultz in the chest.
Police had been responding to a 911 call of a person with a gun and knife, however Schultz was later found to only be carrying a multi-tool knife in their hand, a lawyer for his family said.
On Monday evening the Georgia Bureau of Investigation (GBI), which is leading the inquiry into Schultz's death, said that Schultz had placed the call to 911 emergency responders.
The GBI said that the caller had described to police a white man with long blonde hair, wearing a T-shirt and jeans, and carrying a knife and possibly a gun.
They also claimed to have found three different suicide notes inside the dormitory where Schultz was living.