Flamur Beqiri, 36, was shot dead near his house in Battersea, southwest London, at around 9pm on 24 December as he returned home with his family.
The Metropolitan Police has said the shooting appeared to be a “targeted attack”.
Detective Inspector Jamie Stevenson said the father was shot multiple times by a lone attacker who fled on foot.
“He remains in custody in Denmark pending extradition proceedings back to the UK,” a police spokesperson said.
Beqiri, a Swedish national of Albanian heritage, had been living in London for four or five years.
“We believe Flamur may possibly have been involved in some criminality in Sweden, and are in liaison with our Swedish counterparts to try to understand what, if any, incidents there may have been that might have led to someone seeking retribution against Flamur in the UK,” Mr Stevenson said shortly after the attack.
He was reportedly the brother of former Real Housewives of Cheshire star Misse Beqiri.
In a statement released in December, Beqiri’s family said they were “in a state of shock” over the attack.
“To have so much sadness at this time of the year is heartbreaking,” the family said, as they asked to be allowed to “grieve in peace”.
Neighbours living near the scene of the shooting described hearing multiple gunshots and a woman screaming for help on the night of the attack.
Vittoria Amati, a local resident, said she heard “eight to 10” shots fired in quick succession.
“I then heard the screams of the wife. I came out and realised it was one of my neighbours,” Ms Amati said.
“He was lying in front of his doorway in a pool of blood. He was still alive. We were really hoping he would make it.”
Additional reporting by PA