Chronic fatigue is a debilitating disorder with widespread consequences, but effective treatment strategies are lacking. Novel genetic mouse models of fatigue may prove invaluable for studying its underlying physiological mechanisms and for testing treatments and interventions. In a screen of voluntary wheel‐running behavior in N‐ethyl‐N‐nitrosourea mutagenized C57BL/6J mice, we discovered two lines with low body weights and aberrant wheel‐running patterns suggestive of a fatigue phenotype. Affected progeny from these lines had lower daily activity levels and exhibited low amplitude circadian rhythm alterations. Their aberrant behavior was characterized by frequent interruptions and periods of inactivity throughout the dark phase of the light‐dark cycle and increased levels of activity during the rest or light phase. Expression of the behavioral phenotypes in offspring of strategic crosses was consistent with a recessive inheritance pattern. Mapping of phenotypic abnormalities showed linkage with a single locus on chromosome 1, and whole exome sequencing identified a single point mutation in the Slc2a4 gene encoding the GLUT4 insulin‐responsive glucose transporter. The single nucleotide change (A‐T, which we named “twiggy”) was in the distal end of exon 10 and resulted in a premature stop (Y440*). Additional metabolic phenotyping confirmed that these mice recapitulate phenotypes found in GLUT4 knockout mice. However, to the best of our knowledge, this is the first time a mutation in this gene has been shown to result in extensive changes in general behavioral patterns. These findings suggest that GLUT4 may be involved in circadian behavioral abnormalities and could provide insights into fatigue in humans.