Regional public broadcaster RBB and a local daily said the alarm had been raised at a secondary school in the town of Gosen-Neu Zittau, set in a forested area just outside the German capital.
The Maerkische Allgemeine Zeitung newspaper reported online that the man arrested was 19 years old and the ex-boyfriend of the victim, citing sources close to the investigation.
It said the 30-year-old man was believed to have died while trying to intervene, without specifying whether a knife or other weapon was used.
Police earlier confirmed only that two people had suffered severe injuries, that police were on the scene and that a suspect had been arrested.
"Following an act of violence, a male suspect was provisionally arrested," police said on their social media channels.
"According to current information, he is linked to the incident. We are currently securing the crime scene."
Images from the streets near the secondary school showed multiple emergency service vehicles, while two rescue helicopters were deployed.
The private Docemus school said regular classes would be cancelled Friday but that the school "will remain open to any students who wish to come to the campus", the report said.
"Together with our staff and professional support personnel, we want to provide them with a safe space where they can gather, talk to one another and process what has happened together."
Last month, two girls were seriously wounded and a 16-year-old suspect was arrested after an attack at a secondary school in southern Germany.
Authorities said at the time that the suspect in that attack had been suffering a "mental health emergency".
