Police said the 18-year-old from the Friedrichshain area of the capital was arrested at 1.30pm. Officers said the suspect was known to police.
The man was stabbed in the chest and a police spokeswoman said he died in an ambulance on the way to hospital.
Witnesses said that the man had been walking with two women when they were approached by the attacker.
According to police, the man had just left a nightclub with the two women and another man when they were confronted.
They exchanged a few words before the attacker drew a knife suddenly and stabbed the victim. There was no argument in the moments before the stabbing.
The attacker was described as having a nose ring and three piercings in his lower lip. He was wearing a shirt and baseball cap and white socks.
Police believe he was aged 20 to 25 years old and he was reportedly accompanied by a woman with pink hair.
In recent years there have been several cases of violence around Alexanderplatz. A 20-year-old man, Jonny K., was beaten to death there in 2012.
Frank Henkel, Berlin's senator responsible for policing, said that he was deeply upset “that a young person could be so brutally killed in our city”.
The incident showed that “even with the increased security measures and additional personnel introduced after the death of Jonny K., we can't rule out such unfathomable acts".