Alison Johnson came across the symbol on the popular Sett Valley Trail in New Mills behind the town's leisure centre.
She said she phoned 101 to alert police yesterday - but they advised her to contact the council.
"I'm very upset," she said.
"To me it feels like an offensive hate crime.
"I thought the police would want to investigate this."
Nobody from Derbyshire Constabulary was available to respond this afternoon.
Alison said she has contacted Derbyshire County Council's parks department over the matter.
"They said they are going to look at it," she added.
"They took all the details and took the time to understand my concerns for which I was really grateful."
For centuries the swastika was a symbol of good luck and auspiciousness - before it became associated with the Nazis and racism, hatred and mass murder.
The Sett Valley Trail is a two-and-a-half mile recreational path for walkers, cyclists and horse riders linking New Mills and Hayfield.