The pensioner was pushed to the ground in Drum Terrace Cemetery, near Easter Road, before the man made off with her handbag, which contained more than 100.
A couple in the cemetery rushed to assist the elderly woman before contacting the police for help.
A spokesman for Lothian and Borders Police said: "This is a disgraceful crime committed against an elderly lady in broad daylight.
"I am appealing for anyone who saw this man running from the cemetery and into this area to contact police immediately."
The woman was attacked at around 2.20pm on Saturday when she was tending to her daughter's grave in the cemetery, which backs on to the Easter Road stadium.
Police later found the pensioner's bag near a wall at the B&Q store on Easter Road, although some of its contents were missing.
Police are now searching for the man who is white, aged between 20 and 40 and around 5ft 10in to 6ft tall. He had short dark hair which was greying at the sides and was wearing a beige jacket and dark trousers.
The elderly woman was left shaken but not physically hurt.
Elderly welfare groups have spoken of the attack as "despicable" while warning older people to visit isolated areas, such a this cemetery, only with someone else. Lindsay Scott, a spokesman for Age Scotland, said: "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."
The robbery is the latest in a line of crimes against elderly people in recent months.
In January, a 75-year-old woman had her bag snatched by a man just after 7pm when she was walking near the Mecca Bingo on Manderston Street. The thief was then seen running towards Easter Road.
Last month, an 82-year-old woman was robbed of money in broad day light at a bus stop after shopping at the city's Craigleith Retail Park.
Anyone with information surrounding Saturday's attack is asked to contact Gayfield CID on 0131-620 5125 or Crimestoppers on 0800 555 111.