The woman was out walking her dog in the woods at Västra Kykogarden cemetery at 7am this morning when she came face to face with a large wild boar, according to local newspaper Göteborgs-Posten.
"I have never run as fast in all my life," the woman told the newspaper.
A hunter employed by the Church of Sweden was later able to confirm that in fact two wild boars had been out in the graveyard.
The animals may now be hunted and shot subject to a decision from the council.
Wild boars are not uncommon in Sweden and have in recent months been spotted in several residential areas around Gothenburg.
Sightings have been made in the built up areas of Billdal, Lindome and Mölndal.
Wild boars are normally very shy and fear humans. It is very rare that one would go on the attack and normally only when protecting its young.
While wild boars mate several times per year it is not thought that the animal in question was with offspring.