Murphy, who has appeared just once at senior level for the Canaries, enjoyed a spell with Swindon earlier in the campaign, where he made seven appearances.
The 19-year-old joins fellow Norwich youngster Jamar Loza at Roots Hall and could go straight into the Blues side to face Torquay on Saturday.
Manager Phil Brown told the club's official website: "I'm delighted we've been able to bring in Jacob. He is highly rated by Norwich City and has got that pace we can utilise between now and the end of the season.
"After seeing the impression Jamar made on Monday night, we're hopeful Jacob can do exactly the same. It will help both of the players being here together, having played with each other for so long.
"We've got seven games left this season, and I'm confident Jacob will make a big impression between now and the end of the season."