Patterns of within-host influenza A virus (IAV) diversity and evolution have been described in natural human infections, but these patterns remain poorly characterized in non-human hosts. Elucidating these dynamics is important to better understand IAV biology and the evolutionary processes that govern spillover into humans. Here, we sampled an IAV outbreak in pigs during a week-long county fair to characterize viral diversity and evolution in this important reservoir host. Nasal wipes were collected on a daily basis from all pigs present at the fair, yielding up to 421 samples per day. Subtyping of PCR-positive samples revealed the co-circulation of H1N1 and H3N2 subtype swine IAVs. PCR-positive samples with robust Ct values were deep-sequenced, yielding 506 sequenced samples from a total of 253 pigs. Based on higher-depth re-sequenced data from a subset of these initially sequenced samples (260 samples from 168 pigs), we characterized patterns of within-host IAV genetic diversity and evolution. We find that IAV genetic diversity in single-subtype infected pigs is low, with the majority of intrahost Single Nucleotide Variants (iSNVs) present at frequencies of <10%. The ratio of the number of nonsynonymous to the number of synonymous iSNVs is significantly lower than under the neutral expectation, indicating that purifying selection shapes patterns of within-host viral diversity in swine. The dynamic turnover of iSNVs and their pronounced frequency changes further indicate that genetic drift also plays an important role in shaping IAV populations within pigs. Taken together, our results highlight similarities in patterns of IAV genetic diversity and evolution between humans and swine, including the role of stochastic processes in shaping within-host IAV dynamics.