Sutton, who can play at centre-half or full-back, has made 25 appearances for Rovers this season.
The 29-year-old joined the club last July following his release by League Two side Mansfield Town.
Barrow are currently 17th in the National League table, six points above the relegation zone.
Barrow have signed versatile defender Ritchie Sutton on loan from National League rivals Tranmere Rovers until the end of the season.