Testing and isolation have been crucial for controlling the COVID-19 pandemic. Venezuela has one of the weakest testing infrastructures in Latin America and the low number of reported cases in the country has been attributed to substantial underreporting. However, the Venezuelan epidemic seems to have lagged behind other countries in the region, with most cases occurring within the capital region and four border states. Here, we describe the spatial epidemiology of COVID-19 in Venezuela and its relation to population mobility, migration patterns, non-pharmaceutical interventions and fuel availability. Using an SEI metapopulation model, we explore how movement patterns could have driven the observed distribution of cases. Low within-country connectivity most likely delayed the epidemic in most states, except for those bordering Colombia and Brazil where high immigration seeded outbreaks. NPIs slowed early epidemic growth and subsequent fuel shortages appeared to be responsible for limiting the spread of COVID-19 across the country.