There's a bit more to it.
The link Andrew gave will tell you if the browser supports image embedded profiles, and if so whether it supports v4 as well as v2 profiles. It doesn't tell you if the browser supports monitor profiles. Colour mangement requires both.
Internet Explorer supports image embedded profiles - even v4 - but does not support monitor profiles (not even IE10). It assumes your monitor has an sRGB colour space. Most normal-gamut monitors (i.e. not wide-gamut) are very roughly sRGB, but few are exactly sRGB. This means colours for images with an embedded profile will be roughly right on normal gamut monitors, and hopelessly wrong on wide-gamut monitors (very over-saturated).
Chrome does not support image embedded profiles (it assumes all images are sRGB) but does use monitor profiles. It means it will display sRGB images - and only sRGB images - correctly on any profiled monitor.
Safari supports both image embedded profiles and monitor profiles, so any image with an embedded profile is displayed correctly on any profiled monitor. Sadly, images without an embedded profile will generally be displayed wrongly.
Firefox supports both image embedded profiels and monitor profiles, so any image with an embedded profile is displayed correctly on any profiled monitor. Images without an embedded profile are assumed to be sRGB, so are generally displayed correctly.
Only Firefox and Safari are properly colour-managed, and Safari only for images with embedded profiles.