This was up from 144,400 people, about 2.74% of the population, in the week to October 10.
This equates to around one in 35 people in Scotland for both weeks.
Kara Steel, ONS senior statistician for the Covid-19 Infection Survey, said: “Today’s data show a mixed picture. Though infections appear to have slowed in England and are now declining in Wales, they are increasing in both Northern Ireland and Scotland.
“Infections are highest in those aged 50 and over in England, though there has been an increase in secondary school aged children.
“It remains too early to say from the data whether we are seeing a turning point in the level of infections – which remain high across the countries.”
In England around one in 30 people were estimated to have Covid-19 in the week ending October 17, while in Wales and Northern Ireland the figure was around one in 35.
The Scottish Government said more than 1.3 million vaccines have been delivered to protect against the latest strains of flu and Covid-19.
The Covid-19 vaccine is being given at the same time as the flu jab where possible, and so far 94% of those invited have had both at the same appointment.
More than two million people in Scotland will be offered both vaccines over the next three months.
Health Secretary Humza Yousaf, encouraging people to take-up the booster jabs, said: “Scotland remains steadfast in the effort to protect everyone – continuing the huge success of the vaccination programme since it was first rolled out in December 2020.
“Covid-19 has not gone away and I call on everyone to take up the offer of a booster as soon as their invitation arrives to protect themselves, their families and the NHS.”
Mr Yousaf said the Scottish Government is expecting another wave and urged anyone eligible for vaccination to take up the offer.