Police said in a tweet that one suspect had been detained on suspicion of involvement in the incidents. They released no details on the suspect or the victims.
Prime Minister Mark Rutte said it was not a terror attack, echoing comments from the police.
"It is terrible what happened there. People were killed and others were injured," Rutte said at an EU summit in Brussels.
The incidents happened in a residential neighborhood in the north of Maastricht, a city 215 kilometers south of the capital, Amsterdam, and close to the Netherlands' borders with Belgium and Germany.
Police said the investigations are continuing.