Some of the sites where you can watch new Malayalam movies in full include YouTube.com and IndiaEveryDay.in. Both feature new movies but have older classic Mayalam films as well.
Malayalam cinema, sometimes referred to as "Mollywood," has been in existence since the 1920s and is a large part of Indian culture. In order to make these films available to those of the Indian diaspora, many websites have come into existence that make these films available to the public where Internet is available. YouTube and IndiaEveryDay are some of the main sources of these films. IndiaEveryDay has YouTube videos embedded, so it is not a unique source.