The 26-year-old joined the Shrews in the summer but has made just five starts for the club.
And boss Graham Turner wants the midfielder to get regular football ahead of next season.
He told the club's official website: "At present we have a lot of cover in midfield and Asa hasn't been featuring.
"With the chance of him getting some good game time at Aldershot, we think it's a move that is beneficial for us both."
Hall began his career at Birmingham before moving on to Boston, Luton and Oxford.