Jetstar responded by pointing to their baggage allowance policy.
"Hey, I trust you can appreciate that we do need to implement our policies consistently so we can continue to offer our customers our all day, every day, low fares," the airline tweeted.
That further upset Campbell, with the multiple PGA and European Tour winner calling the airline unprofessional for not addressing him as "Mr Campbell".
Although some followers had sympathy with him, most were surprised at his meltdown - with a few telling Campbell to get over himself.
Campbell announced his retirement in 2015 - nearly a decade after his triumph at the US Open at Pinehurst No 2 in North Carolina in 2005.