There's really two dimensions to this.
Your first concern should be contract language, if you haven't signed a no-compete clause or a contract stipulating that you're not allowed to work in the same industry, or for clients, or whatever - then you're free to do what you want without retribution.
It's often claimed that such no-compete clauses don't stand up well if companies try to pursue them, but I've been involved in cases where there were actual damages paid as a result, so it's best to be careful and/or seek legal advice if you have signed something.
That said, in comments, you mentioned that you have no such contract. That leaves the second factor: culture. This one will be difficult for us to answer. Some service companies enjoy having employees go work for their clients, it's seen as having a "person on the inside" at the client and strengthening the relationship. On the other hand, some employers don't like to lose employees to clients, it's seen as the employee taking advantage of the relationship. Unfortunately, none of us can tell you which situation you're in.
You can try to feel this out for yourself, though. Have other past employees at your current company gone to work for clients? Do you have a good relationship with someone that's been there a while who you could confidentially ask? It's worth putting in the research as long as you can do it in confidence.