All flowering plants have experienced repeated rounds of polyploidy (whole-genome duplication), which has in turn driven the evolution of novel phenotypes and ecological tolerances and been a major driver of speciation. The effects of polyploidy on gene expression have been studied extensively at the level of transcription and, to a much lesser extent, at the level of the steady state proteome, but not at the level of translation. We used polysome profiling by RNA-Seq to quantify translational regulation of gene expression in a recently formed (∼100,000 years ago) allotetraploid (Glycine dolichocarpa) closely related to the cultivated soybean (Glycine max). We show that there is a high level of concordance between the allopolyploid transcriptome and translatome overall but that at least one-quarter of the transcriptome is translationally regulated. We further show that translational regulation preferentially targets genes involved in transcription, translation, and photosynthesis, causes regional and possibly whole-chromosome shifts in expression bias between duplicated genes (homoeologs), and reduces transcriptional differences between the polyploid and its diploid progenitors, possibly attenuating misregulation resulting from genome merger and/or doubling. Finally, translational regulation correlates positively with long-term retention of homoeologs from a paleopolyploidy event, suggesting that it plays a significant role in polyploid evolution.