"Paul suffered a fractured thumb and has been ruled out of action for between 4-6 weeks, he has subsequently been released to Bath rugby for ongoing management," a statement read.
James will miss Wales' two remaining matches, at home to Ireland and away to Italy.
With two victories so far after losing to England in their opener, Wales still have a chance of winning the title.
Captain Sam Warburton had to come off with a bruised knee against France but the flanker will return to training this week.
(Reporting by Martyn Herman; editing by Amlan Chakraborty)
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