He was remanded in custody by the duty prosecutor after a short interview. He is suspected of murder.
“There’s a lot indicating that it was this man,” said Owe Andersson at Sörmland police.
The police are due to search the man’s house on Saturday in the hunt for the murder weapon.
The woman was shot in her home in central Nyköping. According to police she was shot in the chest, and her young child could have witnessed her death.
After the shooting the child is said to have run out into the garden and alerted neighbours.
Both the arrested man and the dead woman are of Vietnamese origin.
“But as far as we know there was no relationship between them,” said police spokesman Kristina Holm to TT.
The child is being taken care of by doctors.