FHM was launched in 1985 under the title For Him Magazine. Zoo was launched in 2004.
An online statement from publisher Bauer Media read: "Unfortunately it's true and it has been announced today the intention to suspend publication of FHM."
The statement added that it had been "an absolute joy producing the magazine over the years".
"Thank you for all your support, we will keep you updated with developments over the coming weeks."
During the 1990s, FHM dominated the men's market and was published in 27 countries, including Pakistan and India.
It claimed that its annual poll of the 100 Sexiest Women in the World "helped propel the careers of many well-known actresses, musicians and models".
The magazine industry has been particularly vulnerable to online competition, and "lads' magazines" have been struggling to hold on to their readers.
In the last 10 years, FHM's circulation has fallen from about 500,000 to below 100,000. In the last 12 months, rivals Nuts and Loaded have both closed their doors.
The publishers said: "Men's media habits have continually moved towards mobile and social." However, it did not specifically blame the online market for its closure.
It said that FHM and Zoo had a combined digital audience of more than five million.
UK men's magazines FHM and Zoo have said they are halting publication.