The car, registered in France, was driving "at a very high speed" in central Antwerp, the Belgian federal prosecutor's office said.
French President Francois Hollande called the incident "an attempted terrorist attack."
"At different times, pedestrians were put at risk," the prosecutor's office said. "When soldiers attempted to intercept the vehicle, it fled."
Authorities eventually managed to stop the 39-year-old French driver and detained him.
Anouk Leemans saw police make the arrest.
"The police chased the man and arrested him calmly," she told CNN via the messaging app WhatsApp. "A crowd quickly gathered but the police were keeping everyone calm."
Leemans said authorities took photos inside and around the car after a bomb robot searched it.
Another witness shot video of authorities taking away the suspect's vehicle.
According to a statement from the prosecutor's office, a pellet-style gun and knives, as well as "a can containing a product still undetermined," were found in the vehicle.
Investigators were looking into any links the man may have had to Islamist extremism but have not yet conclusively determined such ties, the counterterrorism official said.
"He was looking to kill people and to cause something dramatic," Hollande said in a statement.
Belgian public broadcaster RTBF reported the individual detained in Antwerp was too inebriated with alcohol to initially answer questions from police, had drugs in his possession and was believed to be possibly linked to drug trafficking.
Earlier this month, a suspected Islamist extremist
who was shot dead by police after taking a female soldier hostage at Orly airport was under the influence of alcohol, cannabis and cocaine, according to toxicological tests cited by French prosecutors.
The incident comes one day after an attack in London -- which started with a driver plowing into people with a vehicle
-- killed three people.
Wednesday also marked the first anniversary of the Brussels bombings -- the deadliest terror attack in Belgian history
A series of blasts rocked the Belgian capital's airport and a metro station, killing 32 people. ISIS claimed responsibility for that coordinated attack.