A Swedish newspaper confirmed the details of the VIP performance.
The source said the party included Faltskog and Lyngstad singing The Way Old Friends Do.
Ulvaeus and Andersson finished the song with them towards its conclusion, before all four embraced each other.
Andersson said the reunion was a great night, with Lyngstad adding how it was “absolutely amazing” and “very nostalgic”.
The last time the four pop icons were together was in January for the opening of an ABBA-themed restaurant in Stockholm, called Mamma Mia! The Party.