The 18-year-old Barkley joined the Hillsborough outfit in September in a bid to gain greater first-team exposure and has since made seven appearances, scoring in a 2-1 defeat to Bolton.
"Ross has got better and better since he came here," Sheffield Wednesday manager Dave Jones told the club's official website. "The lad has a very bright future and playing games in the Championship will certainly help his development."
Barkley, an England U-21 youth international, will stay at Hillsborough on a week-to-week basis that is authorized under a youth loan arrangement to boost Wednesday in its bid to avoid relegation. Jones' men are currently in the drop zone, sitting 22nd of 24 teams in the Championship.