Dunn was forced to leave the field in the early stages of Bath's 22-12 win over Harlequins on 18 February.
The 24-year-old has scored one try in 15 appearances this season to help the club to fourth in the table.
He made his debut for his hometown team against Calvisano in the European Challenge Cup in 2012, and has since made 41 Premiership appearances.
Bath hooker Tom Dunn will miss the rest of the Premiership season after suffering an ankle injury.