Brian Dowling, 18, was arrested earlier Thursday.
Carson, 31, was stabbed to death early Monday while waiting for the bus with his girlfriend, in what appeared to be a random, unprovoked attack.
Officials say Carson put himself between his stabber and his girlfriend before the fatal attack.
Friday would have been victim Ryan Carson's 32nd birthday. Funeral arrangements for Carson are still pending in Massachusetts.
Dowling has been charged with murder with depraved indifference and criminal possession of a weapon.
Prosecutors also revealed Thursday that the victim's girlfriend failed to pick the suspect out of a lineup.
"The complainant's girlfriend who witnessed the incident was shown a photo array. She picked a different person than the defendant out of the photo array," the assistant district attorney told the judge.
A police official said the girlfriend remains traumatized by the incident and has had difficulty recounting basic details to them.
Two other people successfully identified Dowling from the surveillance video recovered by detectives, which depicts the murder.
Detectives were executing a search warrant Thursday at Dowling's Lafayette Avenue home when he was found inside.
At the home, police sources said detectives recovered the sweatshirt he appears to have been wearing in the surveillance images, along with a knife that will now be tested to see if it matches the murder weapon.
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NYPD Chief of Detectives Joseph Kenny said there were no prior interactions between Carson and his girlfriend and the suspect.
Video that is now a key part of the investigation shows the couple trailing behind the suspect who suddenly kicks mopeds and bikes and asks Carson what he is looking at.
Police say the video shows the suspect pulling out a knife, and as Carson backed up to get away, he stumbled over a bench. While on the ground, video shows the suspect stab the victim.
In that same video, a woman believed to be Dowling's girlfriend, muttered the suspect's first name while apologizing to the couple.
"This is a rage homicide, it's rare in NYC and thankfully so, but a terrible incident," said Robert Boyce, former NYPD Chief of Detectives and ABC News contributor. "Just walking down the street you get stabbed to death. That's really dangerous for the city to incur. People don't feel safe when this happens."
Dowling appeared to be in tears when he was walked from the police precinct on Thursday afternoon. He had no answer for reporters asking why he did it.
Suspect in fatal stabbing of activist walked from police precinct
Despite the break in the case, friends and family are left shattered as they remember Carson's unwavering passion for change.
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"It's incredibly tragic," said Blair Horner, Carson's former boss at the New York Public Interest Research Group. "A life full of promise is snuffed out. And the world is a worse place for it, and we'll miss him dearly."
He is remembered for his selfless acts and outgoing personality.
"I met Ryan when I was 19 and we were both students at Pratt Institute studying writing. Ryan and I actually became close friends because I was experiencing a time in my life where I had nowhere to live and not enough money to eat everyday, to be perfectly frank. Ryan offered me up a space to live, he barely knew me by many measures, and he really helped me through that difficult summer and helped me get back on my feet," said friend Hannah Holden. "That was how our friendship began and that's the kind of person he was, he was so incredibly generous, he was so supportive of people, he was an amazing person."
Carson touched many people's lives and poured himself into everything he did. He was passionate about a grassroots effort he started after his best friend died of a heroin overdose in 2016.
Through No OD NY, he hoped to create overdose prevention centers all over the state, which was just one example of his desire to change the world and make it a better place.
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"He wanted to channel his grief into something that was productive and something that was going to help others," Holden said.
VIDEO | Remembering the life and legacy of a beloved Brooklyn activist:
Remembering the life and legacy of a beloved Brooklyn activist
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