Mr Blair, who had strained relations with the unions when he was prime minister, said he trusted Mr Miliband would handle it in the "right way".
The Labour leader is expected to set out changes to limit union influence in candidate selection on Tuesday.
He says he wants to "mend", not end, links but insists he runs the party.
Labour has referred allegations of union malpractice in the process to select a 2015 election candidate in Falkirk to the police.
An internal party inquiry found evidence union officials signed up new members without their knowledge, breaching party rules, to try and get their favoured candidate elected. Unite leader Len McCluskey has said he has "no trust" in the probe.
Labour has insisted the episode is a one-off but said it showed the need for wider reforms to candidate selection, including a cap on how much any candidate can spend to limit the influence of wealthy backers - whether unions or big business.
There has also been talk of greater use of open primaries to select election candidates - where everyone living in a constituency is eligible to vote whether they are a party member or not.
And some have called for a more fundamental review of Labour's historic financial links with Unite, its biggest backer, and other unions.
Speaking on BBC Radio 4's Today programme, Mr Blair - who clashed with the unions over a range of issues during his 13 years as leader - said it would be wrong for him to be drawn into the dispute.
"I think he (Mr Miliband) is going to make a speech on this and the last thing he needs is advice from me.
"One of my experiences is, when you are about to make a major initiative as leader of the party, the last thing you need are voices off... if you forgive me I am not going to queer his pitch."
Asked whether he was worried the dispute would re-open old divisions in the party and undermine Mr Miliband's leadership, Mr Blair said he was "sure he will deal with it in the right way".
Speaking on Sunday, former home secretary Lord Reid - a close ally of Mr Blair - said the dispute was a battle for the direction of the party, suggesting Mr McCluskey and other union leaders wanted to take Labour back to the 1970s and 1980s.
"I am in no doubt that the leader of Unite wants to impose an ideological direction on the Labour Party that would lead us into political oblivion, as it did in the 1970s and 1980s, and that's why this is a political struggle," he told the BBC.
"Ed Miliband didn't particularly go looking for this fight. This fight came to him," he added.
"But I think he understands, as everyone else in the Labour Party does that a struggle of this nature, which is in essence political, is a determining struggle about the direction of the Labour Party.
"And I have no doubt in my mind that the direction in which Ed Miliband wants to move, which is as I said an open, modern, relevant party."
The Conservatives have said Labour must publish the Falkirk report and refuse to take any more money from the unions until an entirely new system of funding is agreed.
The Conservatives have also asked the Metropolitan Police to investigate claims of criminal wrongdoing in the selection of candidates at two more Labour Party branches.
Party vice chair Bob Neill has written to Met commissioner Bernard Hogan-Howe claiming there is evidence that "merits investigation".
But Unite said the Conservatives were wasting police time and in a "disgraceful political witch-hunt".
"We strenuously reject any suggestion of criminality or that we have broken Labour party rules. Using the police to score political points and diverting their attentions away from making our communities safer is obscene."
And Billy Hayes, the general secretary of the CWU union, said the Conservatives and a "gang of uber-Blairites" were using the dispute to have a go at the unions.
"There's a problem in one contest that needs to be sorted out," he said. "But I'm getting fed up learning through the papers that this or that aspect of the Labour Party's constitution is going to be reformed."
Tony Blair refused to comment on Ed Miliband's dispute with the Unite union, saying he did not want to "queer his pitch" or be part of "voices off".