Wales had capacity earlier on Wednesday, but the site showed “very few” were available later in the day.
PCR test bookings were also unavailable for all regions in England.
Nicola Sturgeon said an administrative error was the cause of the temporary shortage.
Speaking during a Covid update in Parliament on Wednesday, she said: “We are working closely with the UK Government to make sure the flow of testing remains as we need it to be.
“There were steps taken to constrain demand in England last night (Tuesday), which I understand means there are no bookings today for physical test sites in England.
“While that change was being made last night, there was an administrative error made that restricted slots in the other three nations. That has now been rectified.”
At lunchtime on Wednesday, only four out of the 56 walk-in testing sites in Scotland were available for booking a same-day appointment.
These were the Highland Council headquarters car park in Inverness, Mossfield Car Park in Oban, Langlee Community Centre in Galashiels, and Wick Highland Riverside in Caithness.
However, later in the day, the UK Government website said no tests were available in Scotland.
Ms Sturgeon said work is being done to increase testing capacity.
Earlier this week, people in Scotland reported they had to wait up to five days before they received their PCR test result, which normally takes between 24 and 36 hours to come back.
Ms Sturgeon said she hopes the “lengthening turnaround times” will return to normal over the next few days.
“There will continue to be pressure on test but it is important the system continues to flex and respond, and I have got confidence that will be the case,” she said.
Ms Sturgeon said there “will be fluctuations in availability” of tests, adding: “There will sometimes be slots available in spots which are not easily accessible, which is why I would say to people go back and check later because new slots are made available for PCR tests throughout the day.”
The lack of PCR test slots came as Scotland saw a record number of positive Covid-19 results.
A total of 15,849 new cases of coronavirus infections were recorded in the last 24 hours, Ms Sturgeon announced on Wednesday.
This is the highest number of daily cases since the start of the pandemic.
The number is 4,819 more than the previous high recorded on Boxing Day.
The First Minister said the much higher test positivity in recent days may be partially explained by people being more selective about going for a test over the festive period.
Three more people had died after testing positive for the virus, taking the total number of coronavirus-related deaths to 9,836, according to the latest Scottish Government figures.
As of Tuesday night, 679 people were in hospital with Covid-19, 80 more than the previous day, and 36 were in intensive care – a decrease of one.
Northern Ireland’s Public Health Agency (PHA) has urged members of the public to only book PCR tests “when necessary.”
The agency has put in place new PCR test protocols as testing reaches record levels in the country to ensure availability for those who need it.
A spokesperson from the UK Health Security Agency (UKHSA) said: “We are delivering record numbers of lateral flow tests to pharmacies across the country, with almost eight million test kits being made available to pharmacies between today and New Year’s Eve.
“We have made 100,000 more PCR booking slots available per day since mid-December and we are continuing to rapidly expand capacity – with over half a million tests carried out on 23 December alone and delivery capacity doubled to 900,000 PCR and LFD test kits a day.
“If you have not been able to get the test you need from gov.uk, please keep checking every few hours as more PCR and LFD tests become available every day.”