Authorities found a rifle and bladed weapons in the car after the suspect, identified by prosecutors as a 39-year-old named Mohamed R., tried to flee and was detained in the northern city.
The man was "under the influence of something" but it was not clear what substance, a source close to the investigation told AFP.
Authorities were not certain if it was an attempted attack and the incident remained under investigation, several Belgian sources added on condition of anonymity.
The Belgian prosecutor's office said the man was a French national but a French police source told AFP he was Tunisian legally residing in the French city of Lens near the Belgium border.
"He has an address in Lens and as far as we know at the moment, he is not known for large-scale criminal acts," the source said.
"His only previous convictions are minor, such as drunk driving or drug use. He was not on the (French) list of known extremists and according to the initial findings of the investigation had not been flagged up as being radicalised," the source added.
The incident jangled nerves following attacks at Orly airport in Paris and London, and coming the day after the first anniversary of the Brussels suicide bombings that killed 32 people.
"A vehicle with French plates has tried to drive at high speed into the Meir (shopping street) so that pedestrians had to jump aside," Antwerp police chief Serge Muyters told a news conference.
"Our army colleagues forced the driver to stop but he pulled away and ran a red traffic light. We sent a special forces team and the car and the driver were stopped," he added.
"A man in camouflage was taken away."
Images on social media showed investigators searching a burgundy-coloured vehicle near the bank of the Scheldt river.
'Very high speed'
The Belgian federal prosecutor's office said the suspect was driving at "very high speed" and that "at different times pedestrians were placed in danger."
"Different arms were found in the boot, bladed weapons, a pump-action rifle and a container of as yet unidentified liquid," the prosecutor said in a statement.
Bomb disposal experts attended the scene.
"In light of what has initially been gathered, and taking into account what happened in London yesterday, it has been decided to send this case to the federal prosecutor," the statement added.
Belgian Prime Minister Charles Michel said security services in the Flemish-speaking city "did an excellent job" and the government was following this "suspicious incident" closely.
Meir is the main commercial street in Antwerp's historic centre and is mostly pedestrianised. It is one of the country's biggest shopping areas.
The Antwerp incident put Europe further on edge after the attack on the British parliament killed three people plus the attacker, and a man was shot dead at Paris's Orly airport after grabbing a soldier's rifle.
With soldiers deployed at key sites, Belgium has been on high alert since March 22 last year when suicide bombers attacked Zaventem airport and Maalbeek metro station, killing 32 people and leaving more than 320 wounded.
Belgium suffered a further shock in August when a machete-wielding man shouting "Allahu akbar" (God is greatest) attacked two policewomen in the industrial town of Charleroi, before being shot dead.
IS fighters coming home
Islamic State jihadists have claimed responsibility for a number of attacks using vehicles in Europe in recent months, including Wednesday's carnage in London.
An attacker rammed a lorry into crowds in the French city of Nice in July last year, killing 86 people. A similar attack claimed 12 lives at a Christmas market in Berlin in December.
On Wednesday, Belgium's King Philippe and Queen Mathilde led ceremonies commemorating the Brussels bombings, which were also claimed by IS.
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