But he agrees with Prime Minister Tony Abbott that the rules governing MP entitlements need changing.
Mr Burke's taxpayer-funded travel record as a minister is under scrutiny after he led the Labor prosecution of Bronwyn Bishop travel claims, resulting in her resignation as Speaker.
He has admitted flying his children business class to Uluru, at taxpayer expense, in 2012 was "beyond community expectations".
He also charged taxpayers $48,951 for a six-day trip in 2009, including first-class flights for a senior staffer, to attend a Barcelona food security forum as agriculture minister, The Australian said on Friday.
"Mr Burke's conduct has been within the rules at all times and he has my confidence," Mr Shorten told reporters in Sydney.
"I think it is important, though, that we now have a proper review of the rules making sure they do accord with community expectations."
The government has declined to criticise Mr Burke in the wake of Mrs Bishop's downfall.
There was no point in taking pot-shots at individual cases of expenses, cabinet minister Christopher Pyne said.
"I don't see any great benefit of having a running commentary on MPs' entitlements," he told the Nine Network.
"If people stay within the rules, you can't then criticise them."
Mr Pyne's decision to fly his wife and four children business class from Adelaide to Canberra in 2013 has also been queried.
A full review of the entitlements system will be led by former finance department head David Tune and Remuneration Tribunal boss John Conde.
They are expected to be joined by former MPs from both the Liberal and Labor parties and a business person.
The review will examine MPs' travel including to party political events and fundraisers, family expenses and the use of Comcars.
It's also likely to look at the use of VIP air force jets.
"I want this round of controversies to be not just the latest but the last," Mr Abbott told reporters in Tasmania.
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