The 27-year-old left-back has been a regular for the Robins this season and has made 23 appearances since signing a two-year deal in the summer.
He is now recovering from the operation although no timescale has yet been announced for the defender's return.
The Scotland international, who began his career with Blackburn, spent an nine-game spell with Paolo Di Canio's men at the end of last season on loan from Barnsley.
He was part of the Robins' team promoted to League One before moving south on a permanent basis in June.
