Emnes was forced to make an early exit through injury during the first half of his side's 1-0 win at St Mary's Stadium, with Barrow taking his place.
The latter was then taken from the field on a stretcher in the closing minutes of the match, having been the victim of a rash challenge that saw Southampton's Ryan Bertrand receive a straight red card.
Swansea confirmed on Tuesday that Emnes faces a short spell on the sidelines, but Barrow appears to have avoided a layoff.
A short statement from Swansea read: "Barrow has recovered from the injury - on the back of his knee - and took part in training ahead of this Saturday's home clash with Sunderland."
Swansea could welcome back two central midfielders when Sunderland visit the Liberty Stadium.
Leon Britton has returned to training after recovering from a virus, while Ki Sung-yueng - who enjoyed a loan spell at Sunderland last season - is due back from Asian Cup duty with South Korea later this week.
