"This is the first time in history, to my knowledge, that such an act has taken place in the principality," Mirmand, the head of Monaco's government, said.
The Monaco government said the three injured people had been taken to hospital in the nearby French city of Nice.
Monaco's Prince Albert II described the incident as a "heinous crime" and "a shock to the entire Monaco community".
He said "all concerned state services are currently being mobilised" in co-operation with the relevant French authorities.
Yermolaiev is a 58-year-old wealthy real estate developer from Dnipro, Ukraine's fourth-largest city.
He is now a Cypriot citizen after renouncing his Ukrainian citizenship in 2019.
He was sanctioned by Ukraine in December 2023.
He was named the 39th richest Ukrainian by Forbes magazine in 2020, with a fortune of $230m (£173.8m).
