The 24-year-old, who was also released by Redfearn in the summer when at Leeds, has failed to impress following his summer arrival at New York Stadium, making just four starts.
He will stay at Oakwell until January 3 and has been allowed out to get regular football.
Redfearn said: "It is important that the players who haven’t had a clear sight of the first team get regular competitive football.
“If that means going out to get some games then so be it, because if we need to be able to call on them, we know that they have been out playing at a good level.
“Aidy has done that and we will be keeping a close eye on his progress."
White impressed in pre-season after becoming the Millers' first summer signing but failed to take that into the season, being subbed after just 45 minutes of the opening game.
He has barely featured under Redfearn, playing just 92 minutes over the former Leeds boss' first seven games in charge.
“I’m ready for the challenge,” White told Barnsley's official site. “I think we are in a bit of a false position and I’m sure I can help us move up the league table.”
