Anthony Rizzo and Ben Zobrist also homered, and Willson Contreras went 3 for 3 with three RBIs as Chicago won for the fourth time in five games.
Bryant went 3 for 3 and was twice hit by a pitch to reach safely in all five plate appearances. It was his second multihomer game of the season and the ninth of his career.
Arrieta (5-3) allowed one unearned run and five hits in six innings to snap a two-start losing streak.
Travis Shaw had a two-run homer in the ninth for Milwaukee. Eric Thames went 0 for 3 and drove in a run with a groundout before leaving in the bottom of the fifth with leg cramping.