If unsure, consult your manager for advice on handling the situation.
Depending entirely on the nature of the issue, there may be another angle you're unaware of. While there should never be any excuses for somebody's unprofessional behaviour in the workplace, there may be additional sensitivities that could affect the tone, language and timing in your overall approach to the person.
For example, the person may be struggling with some personal and private issues; alternatively, there may be things going on in the workplace involving this person which may not be public knowledge. Just in case there's something you are unaware of, somebody at a management level is more likely to understand the bigger picture.
In some cases, addressing the issue directly with the person may be appropriate, and you certainly can suggest this in your approach to the manager, For example:
"I'm having issues with [X] which is having an adverse effect on me at work. I have been thinking of raising this with them directly but feel that s/he seems to be very emotional at times. I do not wish to accidentally say the wrong thing to her/him and inflame the situation or create a bad atmosphere, could you suggest a course of action?"
You may find out that you are not the first person to have raised the issue; your manager may ask you to approach them, but most managers I've worked with would probably deal with the issue themselves. It is entirely possible that the manager is already aware and has already spoken to them about it before, or they may be completely unaware, in which case there is no harm in talking about it.
In any case, the professional way to approach this is to talk about the issue to your manager - part of a manager's role is to be available to talk to when issues arise between personnel, and to intervene when necessary.