The pensioner was pushed to the ground by the mugger who then stole her handbag containing more than 100 at Edinburgh's Eastern Cemetery.
Police have described the incident as a "disgraceful crime committed against an elderly lady in broad daylight".
Charity Age Scotland said the crime was "despicable and disgusting" and warned elderly people to be careful when visiting cemeteries on their own.
Spokeswoman Lindsay Scott said: "It is particularly callous that this woman was targeted as she tended the grave of her daughter.
"Crimes such as this are very rare but we would advise elderly people to be careful when they are in places such as cemeteries where there may be few people around, making them more vulnerable.
"We would say to them that if they can go with another person, that would be safer. We would also advise them not to carry large amounts of money when they are on their own."
The robbery happened around 2:30pm on Saturday at the cemetery in Edinburgh's Drum Terrace, which backs on to Hibs' Easter Road stadium.
A couple in the cemetery came to the pensioner's aid and contacted the police. Although shaken, the woman was not physically injured.
Officers are asking anyone who saw a man running from the graveyard to get in touch.
A Lothian and Borders Police spokesman said: "On Saturday an 80-year-old local woman was tending the grave of her daughter at Drum Terrace Cemetery near Easter Road, when she was approached by a male who pushed her to the ground and grabbed her handbag containing more than 100. He then made off.
"This is a disgraceful crime committed against an elderly lady in broad daylight.
"Her handbag and some contents were found near to a wall at B&Q at Easter Road some time later.
"I am appealing for anyone who saw this man running from the cemetery and into this area to contact police immediately."
The suspect is described as a white male, aged between 20 and 40 years old. He is about five foot ten inches to six foot in height with short dark hair greying at the sides. He was wearing a beige jacket and dark trousers.
Anyone with information is asked to contact Gayfield CID on 0131 620 5125.
The attack is part of a recent spate of muggings in Edinburgh being investigated by police.
Earlier this month Hearts player Rocky Visconte was attacked and robbed of hundreds of pounds by a knife-wielding gang. The 19-year-old was left with a bruised face after the mugging near Edinburgh's Fountain Park leisure complex.
One of the gang pulled a knife and robbed the midfielder of 300 before the three fled.