The woman was walking on the path close to Canal Street in Saltcoats around 7:30pm on Saturday when she was approached by a man.
Police said he subjected her to a “shocking” assault before making off.
The victim later confided in a relative about what happened. The incident was reported to the police on Tuesday.
There is no description of the suspect.
Detective Inspector Stuart Lipsett said: “Extensive inquiries are under way to establish the full circumstances of this shocking incident and to trace the despicable individual responsible.
“I would appeal to anyone who was in the vicinity of Canal Street between 7:30pm and 8:30pm on Saturday and may have noticed a man following a woman, or anything at all suspicious, to please get in touch.
“Additional patrols will be in the area to provide reassurance to members of the public and I would urge anyone with concerns to approach our officers out on patrol who will be happy to assist.
“Anyone with information is asked to contact the Public Protection Unit based at Kilmarnock via 101.”