Background: With the advances in compact fission power systems and Stirling converters, the efficiency and portability of electrical energy production systems has increased substantially thanks to NASA’s Kilopower project. These 1-10 kWe-class reactors are compact enough to be transportable by pressurized rovers, allowing an extended human reach across the surface of Mars to produce scientific data at a rate that greatly surpasses the rate of robotic rover data collection. If rovers were to harness fission power while mobile, it is possible for near-limitless range. This capability could allow one crew on Mars for under a “Conjunction” class mission as outlined in NASA’s Mars Design Reference Architecture (DRA) 5.0 to visit many geological sites of interest instead of requiring additional landings to explore distant features of the Martian surface. This study explored the parameters that affected the mass of the shielding required to protect the crew against a fission reactor embedded in the chassis of a pressurized rover. Methods: An analytical approach was devised to estimate the required mass of a hypothetical solid tungsten shield under various conditions. Results: Power levels below 3.4 kWe were found to be impractical for rover applications. Between 3.4 kWe and 10 kWe would be able to recharge the rover without returning to base camp. The increase in shielding mass from a 3.4 kWe reactor and a 10 kWe reactor was 6%. The reduction between a 10 kWe reactor at 3 m and 6 m was 7%. Varying the shield thickness in accordance with astronaut activities resulted in a 19% reduction. Powering the reactor off before exiting the vehicle resulted in an additional 65% reduction. Conclusions: Knowledge of the crew activities and locations had the greatest impact on the required shielding mass and the mission activities should be well-understood before finalizing a shield design.