More than 10 bullets hit the car near the village of Lesnyky, around 3 miles outside the capital Kyiv, wounding the driver, a police statement said. It said a criminal case on suspicion of premeditated murder had been opened.
A local television station said at least 19 bullet holes could be seen on the driver's side of the car.
A senior lawmaker said the aide, Serhiy Shefir, was not hurt. Shefir is close to the president, leading a group of advisers.
Zelinskiy, who is in the United States attending the U.N. General Assembly, said he did not know who was behind the attack, but it could domestic or foreign powers.