Gwendoline Goring was sitting in a children's play area after becoming breathless when a warden issued an on-the-spot fine.
After a protest, Central Bedfordshire Council considered the "mitigating circumstances" and rescinded the fine.
Mrs Goring said she was "so glad" as the fine had been stressful.
The council said dog control orders were introduced last October following overwhelming support from the public and town and parish councils.
"They are there to protect people, particularly children, from risks of physical attack as well as to their health if exposed to dog mess," a council statement said.
"In view of Mrs Goring's health issues, we have decided to rescind the fine."
Ms Goring said the incident happened on Tuesday lunchtime as she was walking with her friend in the park.
"I seemed to be getting out of breath and I didn't feel well, and there are no benches at all in that park, except for the two that are in the play area.
"The council has been so grown up about it and I am so pleased as I did not think I would be let off."
An 83-year-old woman has had her fine rescinded for walking her dog in a Dunstable park where animals are banned.