The move threatens eight editorial jobs and four commercial roles already said to be in a two week consultation period.
The last issue of the magazine will be its June issue, which will be on sale on April 23, after which the brand will move to an online only publication.
Maxim, which launched in 1999, has suffered a large fall in circulation in recent years as consumers have shifted away from buying lads' magazines.
Dennis said it will be "bolstering" its online news team.
Dennis also said that it will now become the sole importer of the US edition of Maxim, which it will supply to UK newsstands and subscribers.
According to Audit Bureau of Circulations (ABCs), Maxim's circulation for the six months to December 2008, was 45,951, made up of 34,871 news stand and 11,074 subscription sales. The magazine posted a circulation of 328,463 in 2000 and had a circulation above 107,000 in 2007.
Paul Thomas, managing partner, press, at Mindshare, said: "Given Maxim’s circulation performance over the last few ABCs it’s not a surprise. It had made an effort to change things in recent months but it was too little, too late."
Thomas said that given the current economic climate, there could well be more magazine closures to follow.
He added: "It’s interesting that Dennis is boosting Maxim’s online proposition, they’ve obviously had lots of experience in online-only products already with Monkey. It’s no doubt important Maxim keeps a presence in the UK for its international licenses and the deal in the US."