"Multiple shots fired in Ferguson," the St. Louis Police Department tweeted on Sunday. "Please leave the area of Ferguson and West Florissant."
West Florissant Avenue is where Brown was shot on August 9, 2014.
St. Louis County Police Chief Jon Belmar said police used smoke bombs to disperse the protesters. He denied the use of tear gas canisters by police and said the department did not use rubber bullets.
"The department does not use rubber bullets, and we never have used rubber bullets," he told CNN.
Police, with helmets and shields, pushed crowds back and called in tactical units.
Belmar said there were two shootings Sunday night. One of the protesters, who was shot is in critical condition.
He called on anyone with the video of the shooting to share it with the department.
"We cannot continue, we cannot talk about the good things that we have been talking about, if we are prevented from moving forward with this kind of violence," said the police chief.
He also said one officer was treated for a laceration after taking a brick to the face.
Authorities say they are trying to restore order in Ferguson.
Eighteen-year-old Brown was shot multiple times and killed last year in Ferguson by white police officer Darren Wilson, sparking months of violent protests across the United States.
In November 2014, a predominantly white grand jury — of nine white and three black judges — decided not to indict Wilson for killing Brown.
On Saturday, demonstrators marched in the streets of Ferguson and called for justice.