The mini IKEA KNÖLIG bag turns out to be a surprisingly handy storage case for a spare mask or two. It works for paper masks as well as fabric ones. In the video below, I tested it on my Uniqlo fabric mask (which is the comfiest, btw). The tiny bag can probably fit 2 fabric masks.
Remember to wash the fabric mask and sanitise the bag after every use to keep them virus free.
This enterprising Etsy seller embellishes it with a masked Minnie Mouse.