Caretaker boss Mike Jackson has wasted little time bolstering his ranks following Graham Turner's resignation at the start of last week.
Mendez-Laing becomes the third new face at the Greenhous Meadow following Wigan midfielder Fraser Fyvie and Celtic striker Bahrudin Atajic.
The Birmingham-born former Wolves winger, 21, has made a total of 20 appearances for Posh this season although only three of those have been starts, scoring three goals.
One of those came off the bench to secure a 1-0 victory over Town at London Road in mid-October.
Jackson told Shrewsbury's official website: "He's something a little bit different for us. He's got that pace and power about him, that speed, and on his day he can destroy teams.
"We saw when he came on against us down there, bang, great goal. I've seen him a couple of times and he can make an impact.
"I think he's a good acquisition. He knows this level, League One, and he's local which doesn't mean he's travelling all over the place. He'll be a good addition."