Dutch police said a gunman killed a teacher and a local woman after opening fire in a classroom at a university hospital campus in Rotterdam and a nearby house on Thursday.

The 32-year-old suspect, a university student, fatally shot a 39-year-old woman living in his neighbourhood and seriously injured her 14-year-old daughter, police said in a televised news conference.

After setting the woman's house on fire, the gunman went to the Rotterdam Medical Centre university hospital, where he entered a classroom and fatally shot a 46-year-old teacher. The man was arrested near the hospital, where he also set a fire. His motive was unknown.

"We have been shocked by a horrible incident. Shots were fired in two different places in the city. Many people witnessed it," Rotterdam Mayor Ahmed Aboutaleb said. "Emotions in the city are very high. My condolences go out to the victims."

"The suspect was known to law enforcement and in 2021 he was prosecuted and convicted for animal abuse," said Hugo Hillenaar, Rotterdam's chief prosecutor.

Videos posted online showed police instructing students, some wearing medical gowns, to run outside as heavily armed arrest teams arrived at the scene. One video showed a man in handcuffs wearing what appeared to be camouflage pants.

Police said there were no indications of a second shooter.