In a press release, investigators said the first incident occurred on July 2 at approximately 10:25 a.m. at Alias Grace Park, near Yonge Street and Gamble Road, in Richmond Hill.
At the time, police say a mother and her two young children were in the park when a male suspect approached them.
The suspect then pulled down his pants and exposed himself to the family, police said.
Police said a day later, they received three additional reports of a suspect with the same description being exposed to people in the area of Valmont Avenue and Waterstone Street.
Images of the suspect were released by investigators Monday in an effort to identify him.
He is described by police as a man in his 20s or 30s of East Asian descent. He is five feet seven inches tall, weighs 170 pounds and has short black hair.
He was last seen wearing a white T-shirt, shorts, a black backpack and white shoes, police said.
Anyone with information regarding any of the reported incidents is asked to call York Regional Police at 1-866-876-5423, ext.7241 or Crime Stoppers.