Police said the 20-year-old was detained on Sunday morning over the “completely unprovoked” killing of Sven Badzak, 22, in Kilburn.
Mr Badzak was knifed four times by six men armed with three knives as he went to buy a bagel on February 6.
The Metropolitan Police said two teenagers, aged 17 and 19, previously arrested on suspicion of murder have been released on bail.
Mr Badzak, who was working for his father’s construction company and hoped to do a law conversion course, was waiting outside a shop with his 16-year-old friend when they were both attacked.
His mother, Jasna Badzak, a former Conservative Party activist, said she believes her son was killed in a random attack.
Detectives do not think the victims knew their attackers and have no information to suggest it was a robbery.
Ms Badzak, 49, said her son, who was privately educated at Wetherby and Portland Place schools before attending Roehampton University, had gone to Waitrose to get orange juice and then to a bagel shop when he was attacked.
She wrote on Twitter today: “Honey, my darling Sven Badzak I am so sorry for not being with you and especially for not being given a chance to save your life, but mummy will get them all.
“I promise you! I love you.”
As he and his friend were chased at around 5.30pm, they became separated and Mr Badzak, from Maida Hill, west London, fell to the ground and was stabbed repeatedly.
The 16-year-old also suffered multiple stab injuries but managed to escape into a Tesco in Willesden Lane where staff locked the door and gave him first aid.
He is in a stable condition in hospital.
After reviewing CCTV and speaking to witnesses, Detective Chief Inspector Mark Wrigley said: “The attack happened almost instantaneously, there was no fight in the street. They were attacked on sight in seconds and there is no motive.”
Neither Mr Badzak nor his friend were known to police, said Mr Wrigley.
He added that the suspects are six males, described as both black and white, who travelled to the area “ready for violence”.
Ms Badzak said her son, who had a degree in sociology but wanted to become a lawyer, had met Boris Johnson and other well-known Conservative politicians when he was younger through her campaigning work with the party.
The Prime Minister said “absolutely everything” is being done to tackle violent crime after Ms Badzak, a consultant and financial analyst, called on him to help ensure her son’s killers are caught.
Anybody with information is urged to call police on 101 or tweet @MetCC quoting CAD 5580/06FEB.
Alternatively, information can be provided to Crimestoppers, anonymously, by calling 0800 555 111.