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The process of vaccinating the world population against COVID-19 is expected to take well over a year to complete. As vaccination progresses and population immunity increases, a counteracting relaxation of social distancing measures is observed. The result will be a prolonged period of high disease prevalence combined with a fitness advantage for vaccine-resistant variants, implying a considerably increased probability that a resistant variant will spread in the population. In this paper we propose a spatial vaccination strategy that has the potential to dramatically reduce this risk. Instead of spreading the vaccination effort equally throughout a country, distinct geographic regions of the country are sequentially vaccinated, quickly bringing each to effective herd immunity. Regions with high vaccination rates will then have low infection rates and vice versa. Since people primarily interact with others in their own region, spatial vaccination will reduce the number of encounters between infected people (the source of mutations) and vaccinated people (who facilitate the spread of vaccine-resistant strains). Thus with proper logistic preparations, a spatial vaccination campaign could be highly effective in reducing the global risk of vaccine-resistant variants.