Two people have died and a teenager has been left fighting for her life after a 32-year-old gunman opened fire at a house and the Erasmus University Medical Center in Rotterdam, Netherlands.

The motive for the attacks remains unclear but the gunman — who wore a bulletproof vest and was dressed in combat gear — first killed a 39-year-old woman, and left her 14-year-old daughter in a critical condition at their home.

The gunman then went to the Erasmus Medical Center, where he was a student, and shot a 46-year-old teacher dead before setting a fire.

The incident sparked scenes of panic as staff and students fled the scene.

Dutch special police then stormed the hospital before they arrested the man on the centre's helipad.

Rotterdam's chief prosecutor said the man was known to law enforcement authorities and had been prosecuted and cnvicted in 2021 for animal abuse.

Rotterdam Mayor Ahmed Aboutaleb said the shooting had left the city shaken.

"We have been shocked by a horrible incident," he said.

"Shots were fired in two different places in the city. Many people witnessed it.

"Emotions in the city are very high. My condolences go out to the victims."

Dutch King Willem-Alexander and Queen Maxima expressed their sympathy on social media.

"Our hearts go out to the family and friends of the victims of the violence this afternoon in Rotterdam," the royal pair wrote.

"We also think of everybody who lived in fear during these terrible actions."

The Erasmus Medical Center appealed on social media for people not to go to the hospital, but later said it was reopening. 

ABC/AP