Julie-Ann Finney, who spearheaded a campaign for the inquiry, will share the story of her 38-year-old son David Finney, a navy veteran who died by suicide in 2019.
The inquiry will sit in Melbourne over 10 days from Monday.
Mr Andrews is expected to give evidence about how the Commonwealth and state work together on veterans' affairs.
The inquiry will hear from state government representatives on the support available to serving Australian Defence Force personnel and veterans in Victoria.
In a submission to the royal commission, representatives from the Melbourne-based Hawthorn RSL sub branch warned the state was in desperate need of an all-hours specialist mental health unit.
They say the loss of 24/7 beds available to veterans has cost lives and reduced the quality of care.
The Inspector-General of the Australian Defence Force will also give evidence about the agency's role in ensuring accountability.
The inquiry will examine how the office of the Inspector-General maintains its independence while operating inside Defence.
Royal Commission chair Nick Kaldas said the stories told by people at the hearings made a valuable contribution to the inquiry.
"They highlight the key issues and themes we're focusing on as we develop our final report," he said.
The royal commission was established in July 2021 to examine how the system is failing ADF members and veterans.
After this round, it will adjourn until November 20 in Sydney for more hearings.
Submissions can be made until October 13, with a final report to be handed down in mid-2024.
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