The 20-year-old, who has made three appearances for the Bees this season, will go straight into the Cobblers squad for the game against Dagenham & Redbridge.
"Luke is a centre-forward who is strong and quick and we have watched him for a while," Town manager Aidy Boothroyd said.
"He is one of those players on our Under-21 list who we have done our homework on. With our injuries at the moment we need to add up front and I am sure he can come in and do a good job for us."
Norris spent time on loan at Boreham Wood last season.