Reveal saw circulation tumble 18% year on year to 82,000 a week in its most recent ABC figures for January to June 2018.
"Reveal's sales are no longer sufficient to make it commercially viable," James Wildman, the president and chief executive of Hearst UK, told staff in a memo.
"We’ve explored alternative solutions but as Reveal’s celebrity market is particularly challenged on the newsstand, we cannot see a viable way of continuing to publish the title profitably."
The publisher launched Reveal in 2004 and it sold 347,000 at its six-monthly peak in 2007 -- with the highest-selling issue reaching 570,000 in one week in April of that year thanks to a price cut.
Average print circulation halved between 2007 and 2014 to about 160,000 and has halved again in the last four years.
Hearst UK will consult staff for 30 days, which usually means more than 20 employees are at risk.
It is thought that the owner of titles including Good Housekeeping, Harper's Bazaar and Esquire will redeploy some of the affected employees in other roles.
Staff often work on a number of a titles, rather than a single publication, after Wildman introduced editorial "hubbing" of resources to improve efficiencies last year.
The last issue of Reveal will be published on 2 October.
Reveal and rivals such as Bauer’s Heat and Closer boomed in the mid-2000s in the women’s weekly market, but they have seen their print circulation tumble in recent years as readers turned to news websites such as MailOnline and social media for the latest celebrity gossip.
Big names such as Kim Kardashian have also amassed huge personal followings on Instagram and Twitter that allow them to communicate directly with fans, further undercutting the role of some celebrity titles.
Hearst UK previously closed Reveal.co.uk and another website Sugarscape.com and print title All About Soap in 2016.
The women’s market has been more resilient than the weekly men’s market, which saw a wave of closures several years ago. Lads’ mags Nuts and Zoo stopped printing in 2014 and 2015.
Wildman, the former chief revenue officer of Trinity Mirror, joined Hearst UK in April 2017.
Newly filed accounts at Companies House show the group’s core publishing business increased annual revenues slightly, by £500,000, to £92.1m and moved back into the black with a pre-tax profit of £1m last year.
Pre-tax profit before interest payments was £6.1m compared to a loss of £1.8m a year earlier.
The accounts said Hearst UK increased profits from its continuing operations by "robust cost management" and it continues "to align costs with revenue".
Hearst UK treated revenues from Comag, a joint venture with Conde Nast, as a "discontinued" operation after exiting the distribution business.
Hearst Magazines’ global operation recently appointed a new president, Troy Young, who has replaced David Carey in New York and joined the Hearst UK board.