Cardiff Blues, Roberts' regional team, say he suffered a hyper-extension of his elbow during Wales' 14-12 defeat against Australia six days ago.
He is due to see a specialist, but initial indications are that he will miss the Blues' remaining four Heineken Cup pool games against Montpellier (home and away), Toulon and Sale Sharks.
Wales kick off their RBS 6 Nations title defence against Ireland in Cardiff on February 2.
Roberts returned to Test match action last month after a long spell out of the game recovering from knee surgery.
He was then concussed in the first-half of Wales' loss to Argentina, before going off nursing a hip injury against New Zealand two weeks later.
The Blues, meanwhile, say their Wales lock Bradley Davies is expected to resume training next week.
Davies suffered severe concussion in the opening minute of the All Blacks fixture after he was floored from behind by New Zealand hooker Andrew Hore, which resulted in Hore being cited and landing a five-week suspension.
Wales full-back Leigh Halfpenny, meanwhile, continues to be reviewed by specialists following an injury suffered late in the Australia clash.
Halfpenny was carried off and taken to hospital after complaining of neck pain. He was detained overnight and underwent scans, which showed no serious injury.
Wales' autumn campaign was riddled by injury issues, with wing George North, centre Jonathan Davies, prop Aaron Jarvis, hooker Richard Hibbard and lock Alun-Wyn Jones also among those who missed part of the four-Test series.
Prop Adam Jones and flanker Dan Lydiate, meanwhile, played no part at all due to injuries suffered earlier this season.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.