Two women were taken to The James Cook University Hospital with serious leg injuries after the collision on Saltburn beach, which happened shortly after 8.15pm on Monday.
Cleveland Police say a blue Audi veered off a road and hit pedestrians on the beach, near the pier.
Two other people suffered minor injuries and did not require medical treatment.
A man, who is in his 70s, was arrested at the scene of the collision and police say he has been released on bail while the investigation continues.
Police have not said what he was held on suspicion of, but officers are urging witnesses and anyone who has information about the collision to come forward.
In a statement police said: “Anyone who saw the blue Audi, who witnessed the incident or who may have footage of the incident, is asked to call Cleveland Police on the non-emergency number 101.”