While writing the literature review for my paper, I found another paper which is closely related to my research. Unfortunately, the paper’s publisher is on Beall’s List. Hence, I wonder if citing the paper will have any negative impact on my paper.
Do not think about the journal where the paper comes from. Just forget about it for a while.
Now, read the paper. Even better, be a reviewer for that paper. Evaluate it. Is it a good related work for you? Is it a not-so-good related work, so that you can criticize it? Does it help you to build some hypotheses, etc.? Then, just cite it. Otherwise, don't.
This is what you are supposed to do as a researcher. Build on top of other's work. Bad papers are in every kind of journal. Good papers are, as well.
Beall's list is useful up to a certain point but it has got limitations. One of which, it is a one-man's work. I do not want to criticize the list here because it does not even matter how good that list is. Be your own judge for the work you cite. Where the paper comes from is, in my opinion, the least of the issues you could ever encounter.
As said in the comments: Read the paper and decide on the ground of the content of the paper and not by the reputation of the journal. Don't get me wrong - I do not support predatory or fake journals in any way. But it happens frequently that "quality of the paper" and "quality of the journal" (both understood in a vague sense) do not match. Good journals sometimes publish not-so-good papers and also it may be that the authors of the journal you mention simply were not aware of the listing in Beall's list.
Journals get listed there for various reasons, and there is off course a subjectivity factor. One of Beall's pet peeve is aggressive marketing strategy, which is indeed annoying and suspicious, but has also been frequently used by established publishing groups. Check whether there is a post that describes why this particular journal/publisher is on his list (in this case the post is outdated and does not point out major misconduct).
While the presence of a journal on Beall's list does not in itself mean that the work you read is of bad quality, a lot of the 'journals' listed there have no peer review and no editorial process whatsoever. Most of these 'journals' will publish anything.
Which means that the burden of judging quality is on the reader only, as the other answers pointed out, but also that there are frequent cases of plagiarism. Chance are that the original content has been published somewhere else before, on a preprint server, or a university website as part of a dissertation, or even in a legitimate academic journal. Therefore, if I where you, I would google chunks of the text and make sure that you cite the original version.
Now, from an ethical point of view, a majority of the journals listed by Beall have as business model to pray on the necessity for researchers to have long lists of publications to raise their chances of getting funded or awarded tenure. Citing these, in a way, encourages that sort of behavior, which I personally find harmful to science, dishonest towards funding agencies and taxpayers, and unethical.