Mr Smith, who is challenging leader Jeremy Corbyn, said he wants an honours system that rewards "selfless acts, not political and personal patronage".
Mr Corbyn was criticised for nominating Shami Chakrabarti for a peerage as part of David Cameron's resignation honours.
It comes after questions were raised about the former PM's own list.
Mr Smith, MP for Pontypridd, said Mr Cameron's list - which included many Downing Street staffers and Conservative donors - was put together with "blatant cronyism".
"David Cameron's resignation honours list has brought the system into disrepute and deepened people's mistrust of politics.
"It's simply not good enough for [Prime Minister] Theresa May to turn a blind eye to this situation - we need fundamental reform of the honours system so it can reward good deeds and restore people's trust in politics."
He also said his proposed five-year honours ban would stay in place until a total overhaul of the system was completed.
Ms Chakrabarti, who recently concluded an inquiry into anti-Semitism in the Labour Party, has said she was "honoured to accept [Labour leader] Jeremy Corbyn's challenge and opportunity to help hold the government to account".
But her appointment was criticised by Jewish groups, and Labour's deputy leader Tom Watson said it was a "mistake, because I don't agree with resignation honours".
Marie van der Zyl, of the Board of Deputies of British Jews, said it was "beyond disappointing" Ms Chakrabarti had been offered a peerage by Labour "following her so-called independent inquiry".
"The report, which was weak in several areas, now seems to have been rewarded with an honour," Ms van del Zyl added.
Among those honoured by Mr Cameron were former Chancellor George Osborne, who was made a Companion of Honour, while knighthoods were awarded to Tory MPs Oliver Letwin and Patrick McLoughlin among others.
Mr Cameron's ex-spin doctor Craig Oliver and Samantha Cameron's adviser Isabel Spearman are also on the honours list.
Labour leadership challenger Owen Smith says honours will not be bestowed upon Labour donors, MPs, advisers and staff for five years if he wins the contest.