Detectives investigating the killings at Clark Court, Stonebridge, near Wembley, north London, arrested the man, aged in his 20s, last night.
A Metropolitan Police spokeswoman said: "A man in his 20s has been arrested at an address in N15 [south Tottenham]. He is in custody in a north London police station."
A family friend found the bodies of sisters Lorna and Connie Morrison, 34 and 27, and their mother's partner Noel Patterson, 62, on Friday.
The three were killed during an 18-hour period between 8.30pm on Thursday and 2.30pm on Friday.
Although neighbours spoke of hearing shots on Thursday night, no-one called police.
The friend went to the flat at 2.30pm on Friday and found the bodies in a bedroom, and also nine-month-old baby Christanio Morrison, Lorna's son, who was unharmed.
The family friend, a woman, contacted the sisters' mother, Evelyn Daley, who was working as a carer nearby when the killings happened.
They called the police, and handed over the baby to officers. He is now in the care of the local authority.
A post mortem examination on Mr Patterson gave cause of death as three gunshot wounds to the face and head. Lorna's cause of death was a single gunshot wound to the head.Reuse content