Five others were injured in the incident, which the authorities say appears to be a terrorist attack.
Police are looking for a 37-year-old Turkish man named as Gokmen Tanis and have warned people not to approach him.
Schools have closed and security has been increased while counter-terrorism police work to find the gunman.
Prime Minister Mark Rutte said the country had been "jolted by an attack", which he described as "deeply disturbing".
"We cannot exclude a terrorist motive," Dutch anti-terrorism co-ordinator Pieter-Jaap Aalbersberg told a news conference on Monday.
The tram attack happened at about 10:45 local time (09:45 GMT). One witness told local media that "a man started shooting wildly".
Another witness told Dutch public broadcaster NOS that he had helped an injured woman after the tram came to a stop.
"I looked behind me and saw someone lying there behind the tram," he said. "People got out of their cars... and they started to lift her up.
"I helped to pull her out and then I saw a gunman run towards us, with his gun raised," he said. "I heard people yell 'Shooter! Shooter!' and I started to run."
Counter-terrorism police earlier surrounded a house near the 24 Oktoberplein junction, where the tram attack took place, but no arrests appear to have been made.
A local businessman told BBC Turkish that the suspect had previously fought in Russia's republic of Chechnya.
Jihadist groups, including those aligned with the Islamic State (IS) group, have long operated in the region.
"He was arrested because of his connections with [IS] but released later," the businessman told the BBC.
Meanwhile, the threat level has been temporarily raised to its highest point in the province of Utrecht and extended until 21:00 GMT.
Utrecht University has closed all of its buildings and trains are not allowed to run into the city's central station.
Paramilitary police have been sent to airports and mosques amid increased security concerns.
Utrecht, the Netherlands' fourth largest city, has a population of about 340,000.
Crime levels are low and gun killings are rare, which is the case for much of the country.
Several people have been injured in a shooting in the central Dutch city of Utrecht on Monday morning, police said.
A man opened fire on a tram in the city centre at around 10.45 local time on Monday morning, witnesses say.
The Utrecht police said a square at a tram station outside the city centre had been cordoned off as emergency services were at the scene.
Local media report that counter-terrorism police are at the scene.
'Shooting incident... Several injured people reported. Assistance started,' the Utrecht police Twitter account said.
'It is a shooting incident in a tram. Several trauma helicopters have been deployed to provide help.'
Utrecht is located about 25 miles south of Amsterdam in central Holland.