The fifth highest ever daily total of Covid cases was recorded on Friday, at 3,613, up from 3,367 the day before.
Prof Linda Bauld, of Edinburgh University, said Scotland is “not in a good situation” to have case numbers this high in September.
She is especially concerned that a fresh spike in cases brought on by the recent return to schools may push figures even higher in the coming weeks, and lead to pressure for schools to be closed.
Prof Bauld said she believed the current case increases are likely linked to the easing of restrictions on August 9.
“I’m concerned there will be pressure again to close schools, and everybody wants to completely avoid that,” she said.
“But if we do have really, really large numbers in schools, then I think that's really tricky for the government.”
Prof Bauld added that it was the consequence of rising case numbers that concerns her, in terms of the impact on schools and children, rather than the health impact, as hospital and death numbers remain quite low.
“This is not a good situation, and to be going into September in this situation is concerning,” she said.
“The vaccines are still working, you can see that the cases are heavily concentrated in young people.
“They've been rising for a little while and there are big numbers over the last few days, but we're not really seeing a breakthrough into the older groups in substantial numbers yet. That might change.
“Hospital numbers are still low, but I would expect them to go up. “
Booster Covid vaccines are likely to be advised by the JCVI for the most vulnerable in Scotland, Prof Bauld said, although they may not be rolled out further than that.
“I think it's pretty likely they [the JCVI] will give it to the most vulnerable, people in care homes, people over the age of 70, etc,” she said.
“To what extent they extend down to people in their 50s … I think there’s some reluctance to do that.”
Prof Bauld said Scotland was in a “similar situation” in terms of virus spread to Israel, where restrictions have been reinstated following a sharp rise in cases and a booster vaccine campaign is underway.
However, the situation may be more challenging in Israel as the Delta variant is new there, and so restrictions were eased based on the higher vaccine response to previous variants.
“They had relaxed all their restrictions,” said Prof Bauld.
"A more transmissible variant wasn't something they were necessarily expecting. They expected their vaccines to hold a strong wall against the virus.
“They knew that when they vaccinated people, the vaccines had a pretty good impact on reducing transmission. That's not the case now just because of the new variant.”
At least two preprint studies have shown vaccine efficacy begin to wane in older people in Israel five or six months after their second dose, she said.
This may add pressure for the most vulnerable to be given booster jags in Scotland.
“You can see from their studies, which are largely observational, that there is some evidence of waning immunity,” said Prof Bauld.
“That's why they've been rolling out their booster campaign, and early evidence suggests that the boosters are about 86 per cent effective, so they’re bringing the level of protection back up to that for the over-60s.”
A Scottish Government spokesperson said: "We have taken a cautious, measured and responsible public health approach to the easing of restrictions, guided always by the latest science and medical advice.
"As we have done throughout the pandemic, we will continue to assess all available data about the spread of the virus.”