The 23-year-old has not seen action for the Canaries yet this season as he has been stuck behind Angus Gunn and Michael McGovern in the pecking order, having made 27 appearances for Scottish Premiership side Hamilton on loan last season.
Argyle are currently bottom of the third tier and manager Derek Adams was left without a keeper after injuries to all three of his senior option, so has been granted special dispensation to sign Matthews.
The Gorleston-born keeper is yet to make his senior debut for Norwich and has previously spent time on loan in League One with Burton Albion and Doncaster Rovers.
However, he was recently handed a new contract extending his stay until 2019, with the club retaining an option for a further year.
The Devon club have lost keepers Luke McCormick (ankle) and Robert te Loeke (back) to injury and then saw Kyle Letheren injure his thigh in the first half of a 1-1 draw with Blackburn in midweek, forcing 18-year-old apprentice Michael Cooper into action.
Matthews is likely to go straight into action for the Pilgrims tomorrow, at AFC Wimbledon.
“I don’t think it happens very often,” Plymouth boss Adams said of the injury crisis, talking to his club’s official website. “Certainly not so early in the season.
“We’ve had a lot to deal with – injuries and suspensions – and it’s not getting any easier; we’ve got nine out for Saturday’s game. But we have Gary Miller back from suspension, so we will see how things go.
“To have nine injuries and then play Shrewsbury and Blackburn and do so well (drawing both 1-1) shows you what a strong squad we have. It’s a big positive.”
Matthews, who has 42 senior appearances on his CV in total, has been give the squad number 34