The coveted white suit, worn by Agnetha Faltskog during the pop icon's 1977 Australian tour was taken from the shed in Healesville and, it's thought, later sold at a garage sale.
It's never been returned and nobody knows its whereabouts.
Promoter Dainty Consolidated Entertainment has posted the reward online in the hope of adding the suit to a new multimedia exhibition AbbaWorld heading to Melbourne's Federation Square later this year.
Anything you ever wanted to know about Agnetha, Benny, Bjorn and Frida will be squeezed into 25 rooms of footage, costumes and rare memorabilia from the Swedes' personal collections.
There are also ABBA singalong, dance and music video opportunities for die hard fans.
ABBA remains one of the top three selling artists in the world, having sold 375 million records worldwide, and continues to sell more than three million records a year.
ABBAWorld - which made its world debut in January in London - will have an Australian slant when it arrives in Melbourne.
In 1977, the band attended a civic reception at Melbourne Town Hall where they were given the keys to the city.
They were also met by then Prime Minister Malcolm Fraser and his family who flew from Canberra for the occasion.
Faltskog has described the tour as "the most incredible of all the things that I experienced with ABBA".
"We have probably never received such a rapturous reception anywhere. It seemed the ovation would never end."
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