The shooting occurred on Friday evening in the commune of Langweid.
The man shot dead two women, aged 49 and 72, and one man aged 52, in one apartment, Bild said citing police.
The shooter then broke into a second apartment and wounded a 32-year-old woman and a 44-year-old man.
The 64-year-old suspect has been arrested, the law enforcement said.
The motive behind the shooting is under investigation.
(With UNI inputs)