Many British Nook owners received the news on World Book Day.
The UK versions of the online book shop, Android app and store accessed via Nook devices will all close.
Barnes & Noble said it is teaming up with supermarket giant Sainsbury's to ensure that customers can still access content they have already paid for.
"We thank you for your patronage and are working closely with Sainsbury's to make this transition as smooth as possible," it said in a statement to customers.
Customers must take action by the end of May in order to retain purchased content, it added, with instructions to follow by email.
30%
share of UK book purchases
47% share of adult fiction
Â£393m spent on e-books
Â£1.7bn amount spent on print books
Nook was launched in the UK in 2012 but the market continues to be dominated by Amazon's Kindle, said analyst Ben Wood from CCS Insight.
"It's pretty tragic - it shows that Amazon is the powerhouse in the e-book market despite the best efforts of everybody else," he told the BBC.
"But it's a sensible move - if it's clear that the growth opportunity doesn't exist, it's better to pull out of the market than keep flogging a dead horse."
In its last quarterly results, released this week, the US company said overall sales were down by 1.8% but its net profit had increased by around Â£5.7m ($8m) year on year.
British Nook owner Tim Glenton, from Suffolk, said he had taken advantage of a special offer to purchase a Nook device but regularly used a Kindle.
"It's a shame there's a lack of competition in the market but it's not going to massively change my life," he said of the news.
"Nook never really quite took off in UK."
Barnes & Noble, the US bookseller behind the e-book brand Nook, has announced it will cease selling digital books in the UK on 15 March.