Areas currently in Level 2 are due to move to Level 1 next week under the roadmap for lockdown easing. Glasgow City is currently the only area still in Level 3 restrictions.
However, speaking this morning Mr Yousaf said it may not be possible for restrictions to be eased in all areas on June 7.
He said: “I must be quite frank, there’s other parts of the country that, clearly from the data, give us cause for concern.”
The First Minister is due to update the Scottish Parliament on the move to Level one on Tuesday.
Mr Yousaf also said today there had been a “drastic” decrease in the number of people failing to turn up for their coronavirus vaccine appointments at SSE Hydro arena in Glasgow.
He said he was encouraged by the fact the numbers of “did not attends” had fallen over the last few days.
On the weekend of May 22 and 23, around half of all vaccination appointments at the SSE Hydro were missed.
He said the 18 to 29-year-old cohort would begin to be vaccinated in the greater Glasgow area this week.
A number of drop-in vaccination centres have also been set up in parts of Glasgow affected by the recent outbreak.
Mr Yousaf said: “Unfortunately the weekend before there was a large number of ‘did not attends’ at the Hydro.
“On Thursday and Friday certainly the data that came through to me that was verified certainly show that the numbers of ‘did not attends’ have drastically fallen, which is positive.
“There’s still a lot of people not attending and so we’re putting a lot of effort into that younger cohort.”