The 19-year-old stopper links up with the Bower Fold club for the three-month spell ahead of their season opener at home to Hednesford Town this coming weekend.
"It is a good move for Matty as it gets him regular Saturday football at a good standard," said Rovers Under-21 coach Eric Kinder.
"He'll be playing in the tough competitive environment of the Conference North.
"What it also allows us to do is move David Raya up to the Under-21s. We rate both goalkeepers highly so this will give both players the opportunity to get regular games.
"With the new Under-21 league rules Matty can train with us and is also available for selection if called upon."
Urwin has permission to play for Celtic in the FA Cup, FA Trophy and Cheshire Senior Cup.