Accessing Covid-19 vaccines may be challenging for people with disabilities, the elderly, which are particularly vulnerable to the adverse effects of Covid-19 disease, and the population in rural areas. The utilization of mobile vaccination clinics is studied in this paper to overcome this challenge.  A mathematical model is proposed to route mobile vaccination clinics over a network consisting of a depot, candidate stops, and demand points. Different service levels are considered to ensure that the mobile vaccination clinic is located within a given distance of demand points. The population at demand points is divided into priority groups with varying criticalities and requirements for service levels. An extension to the location routing problem is proposed and an integer linear model is presented that optimizes the routes and stopping points of the mobile vaccination clinics. The objective is to maximize the coverage of prioritized groups while providing high service levels. A case study based on Van province in Turkey is conducted to analyze the proposed solution method. The preliminary results indicate a tradeoff between the prioritization of groups and the network-level effectiveness of the solution.