The 27-year-old, who has not featured for the Canaries since their 1-0 home defeat to Luton in the FA Cup on January 26, will provide cover for Mark Hudson and Ben Turner at the back for City.
Barnett will wear the No 25 shirt for Cardiff and will be available for Saturday's Championship trip to Sheffield Wednesday if the paperwork is completed in time.
Cardiff manager Malky Mackay told the club's official website: "Leon is an experienced defender and will add quality to our ranks over the coming weeks.
"He's quick, aggressive and a combative player - an excellent professional who has been involved in promotion pushes and is a good lad too.
"I've no doubt he'll fit in very well with the squad and I would like to thank Chris Hughton and Norwich City for their help in bringing Leon in, it's very much appreciated."
Norwich have also loaned midfielder Korey Smith to Oldham for a month.
The 22-year-old, who has had previous loan spells with Barnsley and Yeovil, has not played for the Canaries this season and will be eager to experience some first-team action with the League One side.