The only origins I could locate were anecdotal references, along the lines of this:

Pet owners have known about the ability of brewer's yeast ability to repel ticks and fleas for many years.

Dr Peter Barrett claims to know this is garbage, but doesn't provide citations:

Another myth that seems to prevail among travellers is that eating brewers yeast or vitamin B tablets will repel mosquitoes. Again, this is not true so don't rely on your Marmite soldiers to keep you free of bites.

The one article I could turn up in a quick search was a trial on canines, with a negative conclusion:

There were no significant differences in flea counts among the 3 groups during the first 4 weeks of yeast supplemental feedings.

The abstract did indicate some difference between live and inactive yeast counts, but wasn't clear about what this meant, so I'd be interested to read the whole paper. Overall though the title says it all, so I would tentatively suggest that this is just an old tale, with no solid evidence to recommend using this technique to date.