Both the shooter and the victim were brought to hospital by helicopter and are receiving medical treatment, the spokesman said, Reuters reported.
Witnesses to the incident were being interviewed and there was no longer any danger to the public, the spokesman added.
The shooting occurred near the Martinusschule Primary School, but was unrelated to the school, a police spokesman in Bramsche said.
Witnesses informed the police about the incident at around 7.30am local time, mass-circulation daily Bild reported.