The Self-Determination Theory posits that extrinsic reward withdrawal often undermines intrinsic motivation. This undermining effect varies according to the reward category (e.g., monetary vs. praise). However, the mechanism underlying this variability remains unclear, partly because previous studies have conceptualized intrinsic motivation as a single construct without distinguishing liking (intrinsic value) from wanting (motivational drive). Failure to make this distinction may obscure the effects of rewards on each component. We hypothesized that extrinsic reward withdrawal would differentially affect intrinsic value and motivational drive. To test this hypothesis, we conducted functional magnetic resonance imaging (fMRI) on 54 participants who were randomly assigned to one of three conditions: control (no rewards), monetary reward, or social reward. Participants in the monetary and social reward groups played a stopwatch game twice, first with and then without extrinsic rewards. The control group received no extrinsic rewards during the task. We assessed intrinsic value through fMRI-measured activation of the reward system and motivational drive through voluntary engagement during the task intermission. Intrinsic value, measured by activation in predefined reward-related regions, declined in the control group but was preserved in both extrinsic reward groups after withdrawal. Thus, both monetary and social rewards were associated with preserved intrinsic value. However, intrinsic behavioral motivation declined in the monetary group but was maintained in the social group. These findings suggest that extrinsic reward withdrawal differentially influences intrinsic value and motivational drive across reward categories, thereby clarifying the variability of the undermining effect.