The news broke hours after the Ukrainian leader toured newly recaptured territory in the east of the country and declared that Russian forces had been driven out of almost all of the province of Kharkiv.
Mr Zelenskyy said: “I’ve returned from the Kharkiv region — from our Kharkiv region, from the districts that were liberated. As of today, almost the entire region is deoccupied. It was an unprecedented movement of our warriors. Ukrainians once again managed to do what many considered impossible."
He was scheduled to meet European Commission President Ursula von der Leyen on Thursday as she was in Kyiv for meetings with officials to discuss closer co-operation between Ukraine and the EU.
Mr Zelenskyy's spokesman Serhii Nykyforov did not specify when the accident took place but said the president's vehicle had collided with a private car.
“The president was examined by a doctor, no serious injuries were found,” Mr Nykyforov said in a Facebook post.
The accident will be investigated, he said. The president's medics provided emergency assistance to the driver of the other vehicle for whom an ambulance was then called, the Facebook post said.
Mr Zelenskyy's office released the president's routine nightly video message minutes after the spokesman revealed the incident.
On Wednesday, Mr Zelenskyy said towns and villages recaptured from Russian forces had been left devastated, while a major city struggled to contain damage to its water system from Russian missile attacks.
Kryvyi Rih, the largest city in central Ukraine with an estimated prewar population of 650,000, was struck by eight cruise missiles on Wednesday, officials said.
“The water pumping station was destroyed,” Ukrainian legislator Inna Sovsun said on Twitter. "The river broke through the dam and overflowed its banks. Residential buildings are just a few metres away from the river."
The missiles hit the Karachunov reservoir dam, Mr Zelenskyy said in a video address released early on Thursday. The water system had “no military value” and hundreds of thousands of civilians depend on it daily, he said.
Russian forces suffered a stunning reversal this month after Ukrainian troops made a rapid armoured thrust in Kharkiv, forcing a hasty withdrawal.
Mr Zelenskyy made a surprise visit to the city of Izium on Wednesday.
Until four days ago, Izium was Russia's main bastion and logistics centre in the region. The Ukrainian president watched as the blue and yellow national flag was raised in front of the charred city council building.
“Our law enforcers are already receiving evidence of murder, torture and abductions of people by the occupiers,” Mr Zelenskyy told the nation in his address.
“They only destroyed, only seized, only deported. They left devastated villages and, in some of them, there is not a single surviving house.”