Peter Mangs, 38, a Swede, will get a thorough psychiatric evaluation to determine whether he would be sent to a mental unit or prison if convicted, the National Board of Forensic Medicine said.
Besides the one killing and five attempted killings for which he is being detained on probable cause, Mangs has been told he is a suspect in two other attempted murders, the TT news agency reported.
Investigators said they also are looking at a number of earlier shootings.
"The man will remain in custody until December 21. Only then will there be a decision on whether he shall be charged for additional suspicions," Chief prosecutor Solveig Wollstad said.