A warrant for the arrest of the man, in his thirties, had been issued earlier. The woman’s body parts had been found on Tuesday in the Södra Yngern lake, to the west of Södertälje.
The woman had not been identified at lunchtime on Wednesday. Police spokesman Christer Berg refused to reveal the age of the victim.
Divers were searching the lake on Wednesday for further clues and for more body parts. Police said they also planned to take more witness statements.
The man now in police custody lives in Stockholm, and is said to have had access to a blue Fiat Uno, which was seen near the lake. The car was found on Wednesday morning in the Skarpnäck area of Stockholm.
The discovery of the body parts was made after police received a tip-off.
“Police were directed to this place, and observed the body in the water under the ice,” said a spokesman for police in Södertälje.
It was unclear how long the body had been in the water. The area was sealed off so that police forensic scientists could examine the scene. The body has been sent for a post-mortem examination.