The 32-year-old suspect, a university student, shot dead a 39-year-old woman who lived in his neighbourhood and shot her 14-year-old daughter.
The girl died later in hospital, police said.
After setting the woman's house on fire, the gunman went to the Rotterdam Medical Centre university hospital, where he entered a classroom and shot dead a 43-year-old teacher.
The man was arrested near the hospital, where he also started 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."
Rotterdam's chief prosecutor Hugo Hillenaar said: "The suspect was known to law enforcement and in 2021 he was prosecuted and convicted for animal abuse."
Videos posted online showed police instructing students, some wearing white 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 combat trousers.
Police said there were no indications of a second shooter.
