House of Representatives Speaker Milton Dick has set the date for Saturday, April 1, with candidate nominations to close on March 9.
Mr Tudge delivered his resignation letter to the Speaker last week which kicked off the formal by-election process.
The Liberal Party has not yet confirmed its candidate for the seat, but senior party members are pushing for a female nominee.
Opposition Leader Peter Dutton said the candidate announcement would happen in the "not-too-distant future".
"I would very much like - in the democratic process that we have in the Liberal Party - for a female candidate to be selected in Aston, but ultimately that's a question for the division in Victoria," he told reporters in Perth.
Mr Dutton said the Liberals would go into the election as the "underdogs" because the government was still in its honeymoon period.
"I'm confident, ultimately, that we can win but I think it'll be a tough fight," he said.
In a statement on Monday, the Australian Electoral Commission urged people to update their details on the electoral roll by March 6, so they're ready to vote in the by-election.
"If you live in the division of Aston, have recently moved into the Knox council area or are a local resident who has turned 18 then you should check your enrolment details as soon as possible," Victorian state manager Nye Coffey said.
Former Victorian upper house MP Cathrine Burnett-Wake announced last week she would nominate for the Liberals.
Another potential candidate is Melbourne City councillor Roshena Campbell.
Labor confirmed breast-cancer survivor Mary Doyle would be the party's candidate after she was chosen by the division unopposed.
Ms Doyle was selected by Labor to take a second shot at the seat, having won 47.2 per cent of the two-party vote at the 2022 federal election.
The by-election is also expected to feature candidates from the Greens and One Nation and possibly an independent.
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