Recent studies have demonstrated a close resemblance between some handedness patterns in great apes and humans. Despite this, comparative systematic investigations of manual lateralization in non-primate mammals are very limited. Among mammals, robust population-level handedness is still considered to be a distinctive human trait. Nevertheless, the comprehensive understanding of handedness evolution in mammals cannot be achieved without considering the other large mammalian lineage, marsupials. This study was designed to investigate manual lateralization in non-primate mammals using the methodological approach applied in primate studies. Here we show that bipedal macropod marsupials display left-forelimb preference at the population level in a variety of behaviors in the wild. In eastern gray and red kangaroos, we found consistent manual lateralization across multiple behaviors. This result challenges the notion that in mammals the emergence of strong "true" handedness is a unique feature of primate evolution. The robust lateralization in bipedal marsupials stands in contrast to the relatively weak forelimb preferences in marsupial quadrupeds, emphasizing the role of postural characteristics in the evolution of manual lateralization as previously suggested for primates. Comparison of forelimb preferences in seven marsupial species leads to the conclusion that the interspecies differences in manual lateralization cannot be explained by phylogenetic relations, but rather are shaped by ecological adaptations. Species' postural characteristics, especially bipedality, are argued to be instrumental in the origin of handedness in mammals.