Where is Yoruichi's Zanpakuto? Since the beginning, we see Yoroichi does not wield a Zanpakuto, but isn't it strange? Isn't she a Shinigami and the Zanpakuto is so important for them?

It's true that she has her own fighting style, but like Soi Fon, she has the same fighting style, but uses a Zanpakuto.

There was some flashback moments when we saw younger Yoroichi wielding a Zanpakuto:



I imagine she had Shikai/Bankai to become a Captain, so she should be stronger if she uses it in a fight. Maybe she has lost it or something?
There are many THEORIES as to what happened to her Zanpakuto. I'm not sure if I can ANSWER your question as definitely as you'd like, but I can list some possible answers. It's up to you to find the one that you believe most plausible. Or we can wait til old Tite Kubo gives us the answer. 


She gave it up when she left the Soul Society. 


Yoruichi is a part of a very honorable family, so it's almost possible that she would leave her Zanpakuto to symbolize the fact that she's leaving the Seireitei. 
However, a Zanpakuto is a partnership. It's doubtful that somebody could just leave their partner, especially if their Zanpakuto is an animate object. Also, why would she have to give up something that important?

It was stolen.


It's not impossible to believe that after a particularly long bout with some Hollow, or another Soul Reaper, it was taken as a trophy. Or even destroyed? 
However, Yoruichi is an extremely amazing fighter. She couldn't have lost unless she fought something on the level of the Espada.  

She keeps it with her, but sees no point in using it.


This is what I believe. That she just has it set aside and is waiting for an opportune moment to use it. 
However, why wouldn't she have used it by now??? You would think, with all the amazing enemies that have been introduced, she would've pulled it out by now. 
Also, the only reasons she wouldn't use it is if


It is too weak to make a difference in battle and she sees no point in using it
Or, it is too STRONG and she cannot properly control it
Or, she had a falling out with it, and she's not allowed to use it.




Those are just some theories. I believe she wouldn't have gotten rid of it. I think she would've done what Kisuke did. Personally, I think we'll see it one day, along with her Bankai. Sorry that I couldn't answer your question.