Police say the shooting happened in Schiedam near the port city of Rotterdam on Wednesday when police tried unsuccessfully to calm the 26-year-old man.
When an arrest team entered the apartment, the man attacked them and stabbed a police dog, which later died of its injuries.
Schiedam Mayor Cor Lamers issued a statement saying the suspect was a Syrian who had been living with his father in Schiedam since last year.
The confrontation came a day after a man in Belgium attacked and killed two female police officers and fatally shot a passer-by.
