The 18-year-old, who can also play in midfield, has made two first-team appearances for the Blades and also had a loan spell at Stalybridge Celtic where he scored six times.
Calvert-Lewin's arrival follows the sale of Ivan Toney to Newcastle.
"We like what we've seen of him so far, he's enthusiastic and got the ability," said Cobbler boss Chris Wilder.
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League Two side Northampton Town have signed Sheffield United striker Dominic Calvert-Lewin on loan until January.