According to the publication, the quartet joined together to sing Me and I from their 1980 album Super Trouper.
While there is no video footage of the bash, two photos have circulated of the band embracing each other on stage.
The last time they were all together was for the opening of Stockholm's Mama Mia! The Party, which was held on January 20 but they didn't perform on that occasion.
The occasion marked 50 years to the day members Bjorn and Benny first met, with the strong friendship they forged seeing them go on to form ABBA in 1972 with Frida and Agnetha.
The 70s group had previously been offered a mind-blowing $1 billion to reform for a reunion tour.
However, the turned it down because they weren't interested in going on the road again.
Frida, 70, admitted: "No amount of money would change our minds. Maybe we sometimes say it would be good to do a song together again, just a recording and nothing else, but I don't know if that will happen - so don't say that we will."
The group - which split in 1982 - also opted not to perform at their induction into the Rock and Roll Hall of Fame in 2010.
The mini reunion has sparked speculation that ABBA might make a comeback, although nothing has been mentioned yet.
ABBA sold more than 380 million records after winning the Eurovision Song Contest in 1974 in the UK with their song Waterloo, which went on to top the charts in 10 countries.
- Bang! Showbiz
