If it's solid wood (not some plastic or fiber board-- you know, the stuff that looks like wood, but it's actually not solid) you will have fewer issues, UNLESS they use a really strongly scented stain or sealant on it (and you may or may not be able to tell by looking/smelling..it is hard to say for sure..if you CAN smell it, beware).
I would also avoid cedar if it will be near your bird.
I can't say with certainly that there isn't some risk, but solid wood is safer in general, so if you have to choose between IKEA-style furniture and solid wood, go solid wood.
I am always a little cautious with anything brand-new-- especially if I can smell it, but even if I cannot.
Like I said, that's why I often buy used (vintage etc)