However, it has implemented its own recruitment freeze, telling The Scotsman: “The enhanced recruitment controls include the introduction of a temporary pause on new internal and external recruitment in core Scottish Government, though new vacancies can be undertaken in exceptional circumstances.”
Mr Johnson is understood to have told ministers on Thursday that the civil service should be slashed by a fifth.
Unions condemned the move as “an outrageous act of vandalism on our public services”, with one leader warning that national strike action was “very much on the table”.
The SNP said the plans were “detached from reality” and warned Scotland could be hit hard.
The party claimed more than 6,000 reserved jobs in the civil service north of the border have been cut since 2011.
Mr Johnson wants to return workforce numbers to 2016 levels over the next three years.
There were 384,000 UK civil servants employed in 2016 – the lowest number since the Second World War – but this rose to 475,000 at the end of last year.
Downing Street has not ruled out compulsory redundancies.
The Public and Commercial Services union (PCS) is to hold an emergency meeting of its executive committee next week to discuss its response.
General secretary Mark Serwotka said: “This is not about efficiency. This is about the Prime Minister trying to create a smokescreen to detract from his utter shambles of a government.
“He has chosen to cause our cost-of-living crisis and is desperate to point the blame somewhere, and he has chosen to point the finger at hardworking PCS members who kept the country running throughout the pandemic.
“Our members will not be the scapegoats for a failing government. We have our conference in 10 days’ time. Taking national strike action is very much on the table.”
This could include walkouts by staff at the backlog-plagued Passport Office and the Driver and Vehicle Licensing Agency (DVLA), PCS said.
Dave Penman, general secretary of the FDA, which represents senior civil servants, said: “The reason for the civil service’s expansion since 2016 isn’t because the government loosened the purse strings.
"The government needed civil servants to deal with the consequences of two unprecedented events: Brexit and the Covid pandemic.
“To govern is to choose and ultimately this government can decide to cut the civil service back to 2016 levels, but it will also then have to choose what the reduced civil service will no longer have the capacity to do. Will they affect passports, borders or health?
“Without an accompanying strategy, these cuts appear more like a continuation of the government’s civil service culture wars, or even worse, ill-thought out, rushed job slashes that won’t lead to a more cost-effective government.”
Mike Clancy, general secretary of the Prospect union, said the plans represented “an outrageous act of vandalism on our public services.”
He said: “Through Brexit, and then the pandemic, we have never been more reliant in peace time on our civil service.
“Our members are highly skilled and there is a real risk to government delivery from losing their vital expertise.
“The big cuts to public services since 2010 have often proved an expensive error – these proposals risk doubling down on the mistake.”
Jacob Rees-Mogg, minister for Brexit opportunities and government efficiency, said the job cuts would bring numbers back to 2016 levels after extra staff were brought in to help deal with the pandemic and the “aftermath of Brexit”.
He told Sky News: “I know it sounds eye-catching but it’s just getting back to the civil service we had in 2016. Since then, we’ve had to take on people for specific tasks.
“So dealing with the aftermath of Brexit and dealing with Covid, so there’s been a reason for that increase, but we’re now trying to get back to normal.”
He suggested an annual saving of £3.75 billion was "realistic".
Mr Johnson made the demand during an away day with ministers in Stoke-on-Trent, with the government coming under intense pressure to ease the pain of soaring prices.
The Prime Minister told the Daily Mail: "We have got to cut the cost of government to reduce the cost of living."
He suggested the billions saved could be used for tax cuts, saying: "Every pound the government pre-empts from the taxpayer is money they can spend on their own priorities, on their own lives."
Jim Harra, permanent secretary at HM Revenue and Customs, was forced to write to staff apologising for the fact they heard about the cuts in the media first.
SNP deputy Westminster leader Kirsten Oswald said: "These staggering plans from the Prime Minister are completely detached from reality.
"As families and households up and down the country are terrified to open their bills and face soaring energy and shopping prices, threatening a fifth of civil service staff with the sack is shameful.”
She added: "Governments of all political colours have tough decisions to make as budgets are squeezed – but these proposals smack of spite from a Tory government that has demonised the civil service for too long."