Professor Linda Bauld said the recent rise in cases appeared to be levelling off but the time lag of the virus meant hospital admissions would grow in coming weeks.
Daily cases peaked at 4,234 on July 1 following a sharp rise over the previous month.
Speaking on the BBC’s Good Morning Scotland radio programme on Saturday, Prof Bauld said the latest estimates for Scotland’s R number were between 1.2 and 1.5.
She said: “We are still going to see more people in hospital over the next few weeks.
“We know that there’s at least three or four health boards in Scotland that are expressing real concern about their capacity.
“So unless things improve significantly over the next little while, you know the situation does remain really quite fragile.”
Nicola Sturgeon is due to announce the next steps in a statement to the Scottish Parliament on Tuesday.
Prof Bauld said she did not expect the First Minister to reverse the moves out of lockdown but instead maintain a “cautious” approach.
The Edinburgh University academic said there had been a “dramatic” change in the age range of people in hospital with Covid, adding: “It’s much younger people who are in now, we’re obviously hearing concerns from clinicians – I think there are about 11 people in ICU in NHS Tayside, including some younger groups.
“So that is why you hear from the Scottish Government much more caution than what’s happening at England-level.”
Susan Michie, professor of health psychology at University College London (UCL) and a member of both the Scientific Advisory Group for Emergencies (Sage) and Independent Sage, also spoke to the programme.
She expected Boris Johnson to announce an end to all restrictions from July 19 but urge the public to remain cautious – an approach she said would result in “mixed messaging”.
Prof Michie said: “We know from previously in the pandemic that in this sort of situation, a large number of people actually are incredibly sensible and do go by the data, not by what’s said on any particular date.”