The man approached Mr Abbott on Tuesday while he was campaigning at the Knox City shopping centre in Melbourne's east.
As the opposition leader was doing a meet and greet, the man dressed with Mr Abbott's trademark red budgie smugglers shouted:
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"Do you like the cut of my Speedos, Tony?"
The man was quickly swarmed by photographers and retreated into a nearby shop, where he put on an overcoat and made a quick getaway.
Fairfax newspapers reported the man was Conrad French, who holds a position in the ALP's election campaign headquarters and whose salary is paid from a pool created from the taxpayer-funded electorate office allowance of state Labor MPs.
The ALP federal campaign media unit told AAP the man was not a federal campaign staffer but understood he worked in the ALP's Victorian headquarters.
