Estimates from an Office for National Statistics (ONS) surveillance study suggest that around one in 75 people in Scotland caught the virus in the week up to August 28 - up from one in 140 in the preceding seven days.
That figure represents around 72,000 people in Scotland.
The ONS estimates, which only show infections recorded in private households, are at the highest level since surveillance studies began for Scotland in October 2020.
Sarah Crofts, Head of Analytical Outputs for Covid-19 at the ONS, said: “In Scotland we are seeing out highest estimate of infections since we started collecting data last autumn with a notably sharp increase recorded in the week to August 28.
“The results from this kind of surveillance study are critical to allow us to continue to monitor infection levels, especially as we move into winter months.”
Meanwhile, in Wales, around one in 110 people are estimated to have had Covid-19 in the week to August 28, a slight increase from the one in 120 recorded in the previous week - and the highest level since the week to February 6.
In England, ONS estimates remained unchanged, with around one in 70 people in private households suffering from coronavirus.
At the peak of the second wave in early January, around one in 50 people in England were estimated to have coronavirus.
One in 70 is the equivalent of about 766,100 people.
In Northern Ireland, the latest estimate is one in 65, down from one in 40 in the previous week.