Figures from Facebook showed the Government had laid out £30,531 on the targeted posts in the five days since they were launched on September 4 - the same week MPs voted to block a no-deal departure.
The adverts point to information for businesses and members of the public on how to prepare for the planned exit on Halloween.
The campaign has also been featured on other social networks and on posters and billboards around the country since the start of September, as part of a promotional effort reported to be costing the taxpayer around £100 million.
Figures for the spending on those formats are not publicly available, meaning the total amount spent is already likely to be far higher than £30,000.
Facebook began releasing data on ad spending last year, following criticism for how it shared personal data with advertisers and political groups, including Cambridge Analytica.
The platform allows advertisers to pay to target users based on information they have shared on the site, including age, gender, location and interests.
Facebook data also shows that the Brexit Party and the Conservatives have spent the most on their main pages over the past 30 days.
A combined £48,113 was spent on adverts on the Brexit Party and Nigel Farage pages over the period.
The messages included calls for a no-deal exit and, more recently, an offer of an electoral pact with Boris Johnson if he guaranteed a "clean-break Brexit".
Meanwhile, the Tories continued to spend on adverts promising that the UK would leave on October 31, with a combined £28,100 spent on campaigns on the Conservatives and Boris Johnson pages during the 30-day period.
Labour were the next biggest spenders, with £24,584 spent on the Jeremy Corbyn and Labour Party pages.
The messaging appeared to be more mixed - including adverts on fracking, fox hunting and workers' pay - however, many focused on no-deal Brexit and Boris Johnson's plans to prorogue Parliament.
The Liberal Democrats came close behind, spending £24,271 on adverts on their main page, largely focused on stopping Brexit.