The incident happened Saturday in Alphen, about 20 miles southwest of Amsterdam.
Officials have identified the 24-year old shooter as Tristan van der Vlis. Authorities say he had minor run-ins with law enforcement, including an illegal weapons possession charge in 2003 when he was 17 that was eventually dropped.
Witnesses described his weapon as a machine gun.
At least 15 other people were injured in the attack, including an infant. Van der Vlis shot himself in the head after the attack.
Three of the wounded remained in critical condition as of Sunday. The infant's injuries were said to be not serious. Authorities refused to say whether any other children were killed or wounded in the attack and they haven't publicly released a list with the identities of the victims, citing privacy reasons.
Police said they discovered a note from Van der Vlis in his car, threatening bombings at other malls. His mother found a suicide note at the home where he lived with his father near the mall. Neither gave any indication of why he wanted to hurt other people.
The Associated Press contributed to this report.