"He has been remanded in custody suspected of manslaughter," prosecutor Kurt Runhäll told news agency TT.
The 37-year-old's lawyer, Lennart Jemtelius, told tabloid Expressen that his client admits to causing the 27-year-old's death.
"Whether or not he will be convicted of murder remains to be seen," Jemtelius said. He added: "The purpose was not primarily to kill but to silence him since they were fighting and he was the target of accusations which he had a hard time dealing with."
Police had issued a national alarm as they searched for the 37-year-old man, who was arrested on Friday night in the Uppsala region. He was brought to the police station in Karlstad for questioning and admitted to the murder. His lawyer was present when the questioning continued on Saturday. The detention hearings were held Sunday behind closed doors.
The 27-year-old was reported missing on Monday. He was supposed to go abroad on vacation but failed to reach his destination. According to a post on his Facebook page, he was travelling to Cyprus together with his boyfriend, but police said the couple never left Sweden.
When the man's relatives could not reach him, they contacted the police.
On Friday, flowers, candles and greetings were placed outside the murdered man's home, Swedish Radio's P4 Värmland station reported.