The two members of the federal parliament, Labor's Janelle Saffin and a Western Australian Liberal senator, Mathias Cormann, had hoped to be part of the official delegation of five.
Australia's Department of Foreign Affairs and Trade says the delegation will consist of two government officials and three journalists.
"The Burmese authorities requested that officials and media make up the delegation. Accordingly, we asked officials in expertise in electoral systems and Burma's politics to participate along with media representatives. In parallel, we have also requested that the Burmese authorities allow members of parliament to observe the elections - this latter request is still under consideration." a department spokesman said.
One of the journalists in the delegation is respected ABC television presenter Jim Middleton.
Ms Saffin has been an outspoken supporter of Burma's pro-democracy movement.
Ms Saffin says Burma's ambassador in Canberra has confirmed that visas will not be issued.
She says the refusal casts doubt over the whole election process.
"Things like this just add to it not being seen as free and fair," the MP said.
"Look it's not free and fair anyway in terms of the legal framework.
"But it was to be the start of a really open process and you know situations like this certainly do not help that."
Ms Saffin has told Radio Australia's Connect Asia she is at a loss to explain why she was not issued a visa.
"Maybe they decided they don't want MP's from western nations," she said.
"I have been to Burma many times...over the years. I've had visas...to do political things I've done there."
Ms Saffin says she does not believe her connections are behind the decision.
"I know Aung San Suu Kyi. I know people in the current military government...I [have] visited them in the parliament.
"It's just a bit ridiculous really."
The European Union and Canada say they will send observers to monitor the elections, responding to an invitation from the country's government.
The United States, Australia, Japan, and regional bloc ASEAN have also announced they are sending monitors to oversee the elections.
Burma did not allow foreign observers for its last election in 2010.
A total of 48 by-elections will be held on April 1, contested by the opposition National League for Democracy, including its leader Aung San Suu Kyi.
Burma's government is hoping a process that is judged fair will lead to Western sanctions being relaxed.