He and his partially vaccinated colleague, who has tested negative, have now left the state.
Professor Spurrier said police and health authorities had no ability to punish the infected driver now he has returned to Victoria.
"It's disappointing," she told reporters on Friday.
"SAPOL does a fantastic job at checking compliance of truck drivers but it's simply impossible to be stopping every truck."
The driver made two stops early on Friday morning at a Liberty service station in Glenunga and Coles Express in Tailem Bend. Both have been listed as exposure sites.
Professor Spurrier said it was too early to tell if the case would result in community transmission, but the truck driver posed a greater risk because he was unvaccinated.
The case is unrelated to the Adelaide-based truck driver who tested positive on Thursday.
"These cases continue to show us that the threat of Delta to South Australia is real," Health Minister Stephen Wade said.
"COVID is coming to South Australia and we're preparing for that inevitability. We will be ready."
The other infected truck driver, a man in his 20s, routinely drove across the SA border and had tested negative on September 26.
He was tested again on Wednesday night, with the positive result returned on Thursday morning.
While he lives in Adelaide, he is currently in Victoria and complying with that state's isolation requirements.
His family members have since tested negative, while 56 close contacts in SA have been identified from linked exposure sites.
Professor Spurrier said the number of truck drivers testing positive was a reflection of the level of coronavirus circulating in Victoria and NSW.
"I hope I can get through the long weekend without another truck driver coming through," she said.
From 7 October, truck drivers entering South Australia from Victoria, NSW or the ACT will be required to be vaccinated with at least one dose.
More than 50 per cent of adults in the state are fully vaccinated and 67.8 per cent of those aged 16and over are vaccinated with one dose.