The animal, named Zottel, and fellow dwarf goat Mimo were found in the Zurich-Witikon area, said the party.
They had been tied to a tree and smeared with black paint by "extremist delinquents", they said.
Members of a group called Anti-Fascist Action claimed responsibility for the kidnapping.
Provocative campaignThe animals have now been returned to their owner, SVP parliamentarian Ernst Schibli.
"At the moment he (Zottel) and his friend Mimo are a bit in shock, but mostly exhausted and probably happy that they're home," Mr Schibli told Reuters news agency.
The 10-year-old Zottel has been the SVP's mascot since the 2007 elections, when the party ran a poster campaign across Switzerland depicting three white sheep kicking a black sheep off the Swiss flag.
The party then secured nearly 30% of the vote after the provocative campaign.
According to the SVP's website, "Zottel saves Switzerland" and is "against mass immigration".
For next week's legislative elections, the SVP has centred its campaign around the issue of immigration which it believes is out of control.