You may want to follow the instructions from both the other current answers - as this "answer" doesn't address the fonts directly.
Once you have the fonts, you may still have to "tell" LibreOffice about them under Tools->Options->Language Settings->Languages and ...->Writing Aids. If it doesn't see them, then some additional steps may be necessary (probably easy, but I don't know what they would be.)
Long ago and far away, there used to be a font importer for OpenOffice, but that may be a thing of the past.
In addition, you may want to go into your package manager and install libreoffice-l10n-ml. This will translate Libreoffice itself into Malayam.
I did not see them in my package manager, but you would probably want the Malayam packages for the thesaurus, spell checker, and hyphenation as well.
If you don't get everything set with help here, try posting on the OpenOffice/LibreOffice forums. For this question, I would start here: http://forum.openoffice.org/en/forum/viewforum.php?f=101 . (The buzzwords to use (in addition to fonts) would be Malayam localization. That forum is in English, but you may also be able to find support in other languages.)