The 24-year-old has been signed as cover following the news Joe Jacobson will be missing for between four to six weeks after suffering an ankle injury in training.
Collins, who has made seven appearances for Barnsley since joining from Port Vale, goes straight into the squad for the game against Swindon.
"With the injury to Joe Jacobson, I felt we needed another experienced defender to join the squad," Graham Turner told Shrewsbury's official website.
"Lee is still young at 24 years of age but has a lot of league experience. I've worked with him before when he played 16 games for Hereford in the season we got the club promoted.
"This news doesn't stop the search for other players to add to the squad and we are disappointed that we haven't been able to bring in additional faces before the Swindon game."