The 30-year-old has made four appearances for the Shrews, who currently lie 18th in npower League One.
Manager Graham Turner told Town's official website: "We are pleased to have someone of Rob's experience and pedigree with us for another month.
"It's good to have another experienced head in the squad while we continue to come through this difficult period of the season."
Barnsley have a 24-hour recall clause in the loan deal should they wish to bring Edwards back to Oakwell.
- Sports & Recreation