A “positive trend” was beginning to emerge in the data despite daily cases still being high, he said.
Daily cases peaked at 4,234 on July 1 following a sharp rise over the previous month.
Nicola Sturgeon is due to set out the next set of changes to coronavirus restrictions in the Scottish Parliament on Tuesday.
Speaking to the BBC’s Sunday Show radio programme, Mr Yousaf said: “From the data I have seen over the last week – optimistically, I think we can say we are past the worst of the peak, this particular peak.
“Now that doesn’t mean there wouldn’t be another peak in the future but we’re beginning to see a stabilisation and beginning to see the cases level off.
“Still very high I must say, but we’re beginning to see a positive trend.”
The Health Secretary said the government would take a “cautious not cavalier” approach to the new rules, which will begin on July 19.
Mr Yousaf was asked about comments from his UK Government counterpart Sajid Javid, who said cases could reach 100,000 per day by mid-August.
He said: “We certainly wouldn’t want to tolerate that level of cases.”
Mr Yousaf declined to give a number for what the Scottish Government’s worst-case scenario was for daily infections, saying the situation could change quickly between now and mid-August.
Discussing the Test and Protect system, he said additional contact tracers brought in recently had increased capacity in the system.
Turnaround times for the contact tracing system fell below the World Health Organisation (WHO) standard for two weeks in late June and early July.
Mr Yousaf said: “That means the daily system capacity is increased from 1,300 to 3,800 cases per day.
“And the additional 100 staff coming on board, which I just mentioned that daily capacity should go to approximately 5,000 cases per day in the very near future.”
Asked about changes made to the script contact tracers use, he said it had “evolved” over the course of the pandemic in line with clinical advice, saying it had not been altered in order to meet the WHO targets.
Meanwhile, Scotland has recorded 2,048 new coronavirus cases in the past 24 hours, the latest figures show.
No new deaths were recorded, although registry offices are generally closed at weekends.
The Scottish Government’s figures for Sunday also showed the daily test positivity rate was at 11.2%.
A total of 444 people were in hospital with recently confirmed Covid-19, with 40 patients in intensive care.
So far, 3,928,409 people in Scotland have received the first dose of a Covid-19 vaccine and 2,877,326 have received their second dose.