If you're speaking strictly about western society, it would have been around the early 19th century. At this point, men were still using rice powder on their faces for a whiter complexion, but no longer used rouge or other cosmetics. Makeup for women in this century was considered an improper lower class exercise, due to the victorian mores of the time.
As to why men stopped wearing makeup, there was a general movement towards starkness in male dress, made famous by Beau Brummel. The trend was to reject ornate dress male of previous centuries in favour of basic colours and a good tailored fit. Manliness was becoming less about the flowery and more about the stark basics. That trend has pretty much stayed with us until today.
(Please note that the following is true of Britain, but that other societies will have had different experiences of the proliferation of make-up.)
To add to /u/catalot's comment, the rise of the advertising industry and the wave of advances in chemistry in the late 19th and early 20th centuries contributed to make-up's associations with femininity. Print media were especially important in impressing upon women the need to use cosmetics in the early 20th century, and newspaper columnists were ready to advise ladies of how best to apply new products. In 1929, actress Clare Hardwicke declared make-up 'a modern necessity. No woman can do without it.'
This was a new attitude. As /u/catalot said, for much of the 19th century visible make-up was taken as an indicator of low morals, though at this time beauty salons did discreetly sell cosmetics (think skin cream, not bright purple lipstick) on a small scale. It was not until 1909 in Britain that London's Selfridges on Oxford Street began openly displaying rouge.
The change really comes down to ingenious advertising, advances in production that made cosmetics affordable and accessible, and a wide culture of consumerism.
Interestingly, by the interwar period make-up had in Britain become so exclusively associated with women and femininity that for a man to simply be in possession of a powder puff could land him in jail. Queer men, who at the time frequently described themselves as having a feminine nature, adopted women's use of make-up to express this femininity. Under the 1885 Criminal Law Act, any type of 'gross indecency' between or among men was illegal. Prostitution, also, was illegal.
Thus comes the case of Thomas B., arrested on the Strand in 1924 for 'importuning male persons for an immoral purpose' after he was discovered 'accosting' (probably meaning 'speaking to') multiple men in the area whilst in possession of a mirror, powder and a powder puff. These cosmetic objects only strengthened the Crown's case against Mr B., as 'the man who owned a powder puff was effeminate; the effeminate man possessed illicit sexual desires; such a man was, in police jargon, of the "male importuning type".'
The case of Thomas B. serves as an indicator of the strong associations between cosmetic paraphernalia and femininity in the interwar period, and the ways in which mainstream female uses of make-up could be queered.
Source: Matt Houlbrook, '"The Man with the Powder Puff" in Interwar London', The Historical Journal, 50 (March 2007), 145-171 <http://www.jstor.org/stable/4140169> [accessed 23 January 2014].