As Labor's national executive prepares to meet on Wednesday to find Senator Kitching's replacement, Mr Danby said allegations she was bullied and ostracised by the party's Senate leadership team should be independently examined.
"Australians expect (Labor) to be consistent with allegations of bullying," he told the Nine Network on Wednesday.
"They rightly were upset on behalf of Grace Tame and Brittany Higgins, and it's one of our own sisters in our own camp who's been badly treated in Canberra and treated worse in Victoria by some of the faceless men."
Mr Danby, who served in parliament for Labor from 1998 to 2019 and was a friend of Senator Kitching, said her alleged treatment was terrible and uncalled for.
He called for Opposition Leader Anthony Albanese to address the issue.
"Anthony has got character ... and he's been very pragmatic, but I think he should square his shoulders, face this problem and be consistent as the Australian public would like," he said.
"We can't have one law for people who are disadvantaged in the conservatives and another law for our own people."
Senator Kitching was laid to rest this week following her sudden death, aged 52, from a suspected heart attack in Melbourne on March 10.
The Senate will have a special sitting on Monday, at the request of the leaders of the government and opposition in consultation with other senators, to enable senators to speak on a condolence motion for Senator Kitching.
Meanwhile, the ALP national executive will on Wednesday discuss the Victorian Senate ticket and candidates for two lower house seats.
Labor has not won three seats at a half-Senate election in Victoria since 2007 and is likely to pick up two seats at the coming election expected in May.
Victorian government minister Natalie Hutchins and human rights barrister Fiona McLeod have been flagged as possible replacements for Senator Kitching, who was up for re-election.
Veteran senator Kim Carr is also up for re-election, but faces a challenge, with union leader Linda White tipped to take his place.
With Anthony Byrne retiring from the lower house federal seat of Holt there is speculation Jo Briskey, from the United Workers Union, could replace him as the candidate.
Finding a candidate for the NSW seat of Parramatta is also on the agenda, following the retirement of Julie Owens.
There are suggestions Andrew Charlton, who was an advisor to former Labor prime minister Kevin Rudd, could get the nod.
The ALP national executive will also be asked to institute a Kimberley Kitching Human Rights Award, to be handed out at each national conference to a member who has demonstrated an "outstanding commitment to the advancement of human rights in Australia or globally".
Planning is also underway for an ALP national conference in the second half of 2023.
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