In the same Times story, Professor Karol Sikora, a former head of the WHO cancer program explains, "Moisture makes masks porous, and because of this, all types of mask are essentially vulnerable in damp weather." And disposable surgical masks might be the most affected. Professor Paul Hunter studies Medicine at University of East Anglia and describes disposable masks as being "essentially made out of paper" (via HuffPost). When dry, these masks have a barrier between the paper layers that helps block respiratory droplets, but as it gets wet the whole works begins to disintegrate.
Even N95 masks get low marks in wet weather, leading health professionals to widely recommend that you change any mask for safety after it gets wet. And the WHO concurs, suggesting people "replace masks as soon as they become damp with a new clean, dry mask" (via Yahoo! Sports) There is also a risk of "potential self-contamination that can occur if medical masks are not changed when wet, soiled or damaged." Bottom line: If your mask becomes damp, stay safe by reaching for a new one.