Vaccines have proven to be extremely effective in preventing the spread of COVID-19 and potentially ending the pandemic. Lack of access caused many people not getting vaccinated early, so states such as Virginia deployed mobile vaccination sites in order to distribute vaccines across the state. Here we study the problem of deciding where these facilities should be placed and moved over time in order to minimize the distance each person needs to travel in order to be vaccinated. Traditional facility location models for this problem fail to incorporate the fact that our facilities are mobile (i.e., they can move over time). To this end, we instead model vaccine distribution as the Dynamic k-Supplier problem and give the first approximation algorithms for this problem. We then run extensive simulations on real world datasets to show the efficacy of our methods. In particular, we find that natural baselines for Dynamic k-Supplier cannot take advantage of the mobility of the facilities, and perform worse than non-mobile k-Supplier algorithms.