Faletau has been ruled out of the matches against England, France and Scotland with an injury sustained playing for Cardiff against Ospreys on January 1.
The 35-year-old, who missed the Autumn Nations Series because of a knee issue, is not expected back until late February.
"It's not clear on his return but we're definitely looking at the middle of the Six Nations," Cardiff coach Corniel van Zyl said.
Wales were already set to be without captain Jac Morgan and centre Max Llewellyn for a large chunk of the Six Nations.
Head coach Steve Tandy is due to name his Six Nations squad on January 20.
Wales begin the Six Nations against England at Twickenham on February 7th - their first match since a record 73-0 home defeat by South Africa in Cardiff in November, their 21st loss in 23 Tests.