Mr Abbott, a prominent figure in the "no" campaign during a poll on the issue, says the man asked to shake his hand before assaulting him as he left a newspaper office in Holbart, Tasmania.
The man, who was wearing a "vote yes" badge, said Mr Abbott deserved it "for all the things he said".
Australia is holding a two-month poll on whether to allow same-sex marriage.
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The issue has prompted fierce debate in the country, with Mr Abbott - who described the attack as "politically-motivated violence" - suggesting the incident in Hobart showed how nasty it had become in recent weeks.
"It was very disconcerting to find that the Love is Love brigade, or at least someone who was advocating a "yes" vote, should under the guise of shaking your hand actually give you a so-called Liverpool kiss," he told Sydney radio station 2GB - before assuring listeners his assailant "wasn't very good at it", having left him only with "a very, very slightly swollen lip".
Alex Greenwich, independent MP and the co-chair of Australian Marriage Equality, was quick to denounce the incident.
"There is absolutely no place for violence in the marriage equality debate," he wrote on Twitter. "This is about treating people fairly and with respect & dignity."
It is unclear whether the incident has been formally reported to police, with the local force telling broadcaster ABC they had heard the reports and were making inquiries.
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