Workers are striking in Sydney, Melbourne, Brisbane, Perth and Adelaide and plan to take further action unless the company agrees to improve safety in its supply chain.
The Transport Workers Union says Aldi has not responded after being served a claim, alongside 39 other major retailers, manufacturers and agricultural companies, asking them to commit to safe supply chain principles.
Those principles include accountability for safe work in supply chains, transparency over contracts to protect workers, ensuring workers are able to speak about pay and safety, enhancing safety education, eliminating risk-taking incentives and equipping drivers for natural disasters.
TWU assistant national secretary Nick McIntosh says the German supermarket giant's refusal to lift the safety standards of its supply chain is inexcusable.
"The deadly pressure on drivers and operators is building every day and workers will not accept silence from companies like Aldi who refuse to come to the table on safe supply chains," he said on Thursday.
"When you've got wealthy clients like Aldi pushing drivers and operators to the brink, and gig giants like Amazon exploiting thousands on rock-bottom rates, it's no wonder this industry is in crisis."
The TWU says Aldi has not responded to a claim, served 14 weeks ago, nor has it met with the union.
"For them, it's literally a matter of life or death, with every day that Aldi refuses to act another day truck drivers and operators are under deadly pressure," Mr McIntosh said.
The union says there is an ongoing crisis in the transport sector which contributed to the collapse of Scott's Refrigerated Logistics, which was the country's largest cold chain operators, and start-up Milkrun, which had the backing of tech billionaire Mike Cannon-Brookes.
AAP has contacted Aldi for comment.
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