According to De Broglie, wavelength = h/mv, then for a stationary object, mv = 0, so is wavelength = infinity?

Wow! This is a really hard question! I hate questions like this because they distort the principle of the whole deal. I certainly can't give you an answer what the wavelength would be, but maybe I can give you an answer for the question itself. Whenever you deal with goofy questions like this you have to deal with two ideas: (1) the principles of quantum physics are difficult to generalize to the macroscopic level (even at the micron level and, God forbid, to support ideas like "The Secret," and (2) whenever you get a curveball like this, apply some other equation that doesn't easily generalize, like the Heisenberg Uncertainty Principle (HUP.)

You say, "mv=0", I say, "(dx)(dp) ~ h" (this is the HUP part.) My part says that you CANNOT establish that mv=0, because that would mean that dx ~ infinity, i.e. you don't know where it is, so how did you measure p, the momentum. As a result, if you say, "mv=0," I say the HUP is violated and the universe explodes (well, not really.) and therefore the DeBroglie wavelength (DBL) cannot be infinity.

On a more hand-waving level, for mv = 0, v would have to be 0 for particles with actual mass (although photons can be considered to have momentum too.) For this to be true at any instant, there would have to be absolutely no motion. This might be true at 0 K, but no such condition exists in this universe, as far as I know. Therefore, mv is never 0, and wavelength is never infinity.

Try asking this one in the physics topic. They may be able to give you a better answer.