It's offgassing VOCs. It's the same thing as "new car smell" and "new shoe smell." It's from being shrinkwrapped immediately after manufacture; the gasses haven't had a chance to evaporate.
The smell will dissipate, but no amount of washing or deodorizing will speed up the process. If it's at all possible, store it outdoors until the smell abates. You mentioned you live in an apartment; do you have a balcony or porch of some kind? I would worry less about the sun warping the mat than the bombardment of VOCs in your home.
In the future, buy unwrapped mats. :)