Journals may have differing opinions about the what exactly you may be allowed to reference. However, in most cases, I would expect that there would be no explicit prohibition on citing sources other than traditional academic references. Obviously, if possible, you should cite something peer reviewed, or (failing that) an academic preprint. However, sometimes such things are not available.
I have come across a number of useful citations to things that would not be considered normal academic sources. Sometimes people cite conference presentation slides containing of preliminary results, which have not been published, but which somebody managed to capture a picture of with a smart phone camera. Sometimes a result may be announced in a press release by a laboratory, well before the scientific details are made available to the research community. (A short news piece in a journal like Science would be of a similar character.) These are perfectly reasonable things to cite, if they are the only available sources of information.
Sometimes, I have seen even weirder citations. In one paper my advisor published (which was a topical review relating to some work that had gotten a fair amount of media exposure), he cited a number of reactions to the subject in non-scientific media. That included a comic strip, the Web site for a cult, and a statement by Lyndon LaRouche. So even pretty outlandish things can occasionally be cited in legitimate (if somewhat less serious than usual) academic publications.