The blaze broke out in the early hours at the Vondelkerk, a tourist attraction that has overlooked one of the city's top parks since 1872.
The 50m high tower collapsed and the roof was badly damaged but the structure was expected to remain intact, Amsterdam authorities said.
The head of the Dutch Police Union, Nine Kooiman, reported an "unprecedented amount of violence against police and emergency services" over New Year's Eve.
She said she herself had been hit three times by fireworks and other explosives as she worked a shift in Amsterdam.
Shortly after midnight, authorities released a rare country-wide alert on mobile phones warning people not to call overwhelmed emergency services unless lives were at risk.
Reports of attacks against police and firefighters were widespread across the country. In the southern city of Breda, people threw petrol bombs at police.
Two people, a 17-year-old boy and a 38-year-old man, were killed in fireworks accidents. Three others were seriously injured.
The eye hospital in Rotterdam said it had treated 14 patients, including ten minors, for eye injuries. Two received surgery.
It was the last year before an expected ban on unofficial fireworks, so people bought them in massive quantities.
According to the Dutch Pyrotechnics Association, revellers splashed out a record €129 million on fireworks.
Some areas had been designated firework-free zones, but this appeared to have little effect.