The 20-year-old will be a part of the Shropshire-based League One side until the end of the season.
Street has progressed through the ranks at Palace, playing at various age groups before becoming a key part of the Under-23s side which won promotion to the Premier League 2 Division 1 in the 2020/21 season.
Since then, he has experienced loan spells at Torquay and Newport County, and also featured in the pre-season tour squad of Australia and Singapore.
Commenting on the move, Street said: “Playing for Shrewsbury will be a great experience that I’m looking forward to. Hopefully I can adapt to the standard required in League One and hit the ground running at New Meadow.”