The 19-year-old will spend the rest of the season at the New Meadow and could make his debut in Saturday's League One game against Rochdale.
Ramsay made his Premier League debut against Manchester City in December 2018 and also played against Derby in the FA Cup last season.
"It's another key step in my career," he told the Shrewsbury website.
"Hopefully I can get as many minutes as possible and help Shrewsbury climb up the table. I will be working as hard as I can to cement a place in the team."