First, note that there isn't really a concept of a full directory. Directories themselves don't have a space limit (unless it's a network share that has some quota, but that's a completely different thing). It's the logical/physical disk where the directory resides that has a space limit.
So really, if you want to know if you have enough space to store something, you need the check the disk, not the directory. There is no tool for that in matlab. You could query the size of all the directories as per Siva's answer, or go through Java, .Net (if on windows) or system commands but it is the wrong approach anyway.
Because you have no control over what happens the file system, it may well have become full between the time you asked if there was space and the time you attempt to write to it (however short that interval is). Asking beforehand is pointless. The correct approach when dealing with file system operations is simply to try them and check that they succeed:
[fid, errmsg] = fopen('somefile', 'w');
if fid == -1
error('failed to create file because: %s', errmsg);
error('failed to write file because: %s', ex.msgtext);
Note that this is true of any file operation. There is no point checking that a file exists before using it as some other program may have deleted it in between the check and the moment you use it, there is no point checking that you have permission to write somewhere since some other process may have changed the permission in between. Just try the operations and handle the failure appropriately.