The 22-year-old, who has represented Scotland at various youth levels, has not started for the Championship side this term.
He started his career with Kilmarnock, joining Cardiff from Everton following three separate loan spells.
Kennedy has played 19 times for the Bluebirds in all, starting nine games since joining them in February 2015.
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League Two Plymouth Argyle have signed Cardiff City winger Matthew Kennedy on loan for the rest of the season.