Should I inform my potential advisor that my paper got rejected? I am a recent M.Sc. graduate and I have applied for a few PhD programs abroad.

A few months ago, we submitted our paper (which was about my thesis results) to a journal and also uploaded it to a pre-print server. Then, I mentioned the paper in my CV with the status "submitted to journal X". In my Skype meeting with a potential advisor from a university abroad, I mentioned the fact that we submitted the paper and we have not been notified about the result yet. Then, I sent the link of the paper on pre-print server to him according to his request.

Today, I got informed by the journal's editor that our paper got rejected from journal X. Now I don't know if I need to tell this fact to the potential advisor in our next Skype meeting or through other mediums like email? In general, I guess he will not ask about the status of our paper. If he asks about it, I definitely would answer truthfully. But I don't know should I tell him about the rejection even if he does not ask about it?

Actually, the journal quality is very high and we believe that we can publish our paper in another good journal elsewhere. However, the professor is from a different field and he may not know how hard it is to publish in journal X. Thus, I think that this news unfairly ruin my admission chance.
I don't think that being rejected by a top tier journal of your field should reduce your chances to get the PhD position in any way. Your potential advisor most likely knows this all too well. This is part of the scientific professional life. I would assume that s/he can judge the work you did regardless of his field of expertise our whether it got accepted or not. But if it was well written, presented in a clear and structured way, he or she will appreciate that because it is such an important skill. 

You don't need to mention it yourself if you feel uncomfortable about that. However if you want, you can say that you got rejected by X, but think that with the feedback you got you can really improve the manuscript and will try to publish it elsewhere. This will show your motivation. Most likely your advisor will be happy about that.