The Munster center has sustained knee ligament damage after twisting his knee in the turf and after undergoing scans is now set to see a specialist to discover the extent of the problem.
It means Garry Ringrose could come into the Irish midfield for the games against Scotland and England as they go in search of only their Grand Slam.
"Chris Farrell received treatment on the field earlier today after twisting his knee in the turf,' said the Irish Rugby statement.
"He subsequently jogged on to rejoin the rest of the playing group and felt well.
"He was sent for a precautionary scan this afternoon, which indicated some ligament damage had occurred and he will now see a specialist. Chris is unlikely to be available for the remainder of the Six Nations."