Police had staged a massive manhunt in and around the city of Leipzig over recent days for Uwe Kolbig, 43, who had several child abuse convictions dating back to the days of communist East Germany.
Kolbig jumped in front of a streetcar in suburban Leipzig at about 12:45 a.m. (2345GMT) in an apparent suicide attempt, police said. He was taken to a hospital with serious injuries, the AP says.
Authorities launched the search after they found footage from a security camera that appeared to show him sitting next to the boy on a streetcar in Leipzig last Thursday, the day the boy disappeared while returning home from a day care center.
The boy's body was found Saturday in a garden used by Kolbig. Police say he was strangled after apparently being sexually abused.
The manhunt involved more than 100 officers, tracking dogs, a helicopter with infrared sensors and mounted police.
Prosecutors have said Kolbig was sentenced to two years in prison in 1998 for the attempted sexual abuse of a child. They said this week that he also had been convicted four times of child abuse in East Germany.