A man has been charged after he allegedly indecently exposed himself to numerous women on the popular Bay Run in Sydney's inner west.

Police say the man, 29, approached the women around Glover Street Sports Ground in Lilyfield on three separate occasions between January 31 and February 17.

Leichhardt police launched an investigation and arrested a man at a home on Lawrence Street at Freshwater about 1.15pm on Tuesday.

Officers also searched the house.