Five men attacked the Riau Police headquarters on Jl.
One officer was killed by the speeding vehicle and two others were wounded in the incident, they added.
One local journalist at the scene sustained minor injuries in the attack, police said.
"When the auto broke through into the Riau police headquarters, it was blocked by policemen", national police spokesman Seyto Wasisto told a televised news conference. Police found the van not far from the location of the attack and searched it for possible explosive materials.
In the ensuing chaos, at least two suspected terrorists, both wearing balaclavas, were spotted getting out of the auto wielding sharp weapons and attacking police officers.
This footage shows the police station from the view of a passing driver.
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The attacks are the worst in the world's biggest Muslim-majority country since the bombing of tourist-packed restaurants in Bali in 2005.
Media said one attacker may have had a bomb strapped to his body but police did not immediately confirm the reports.
The attack followed multiple terrorist strikes recently in the country, including the riot in a jail in the capital last week, suicide bombings in three churches on Sunday in Surabaya city, the provincial capital of East Java, and a suicide bombing in the police headquarters in the city, which left at least 28 dead with dozens injured.
The next day, militants attacked Surabaya city police headquarters.
Police said the men belonged to a local extremist group, but not Jamaah Ansharut Daulah (JAD), which authorities believe was behind the family suicide bombings.
The Islamic State (IS) group has claimed the attack via its news outlet.