Reddan fell awkwardly beneath a tackle in the final minute of a compelling match at the Aviva Stadium and was administered oxygen before being carried off.
Ireland's injury-depleted ranks were swelled even further by a number of other casualties with lock Donnacha Ryan damaging his shoulder and centre Luke Marshall sustaining concussion.
Both are doubts to face Italy next Saturday, while flanker Peter O'Mahony, scrum-half Conor Murray, centre Brian O'Driscoll and wing Fergus McFadden also picked up a variety of knocks.
Already missing were lock Paul O'Connell, wings Tommy Bowe and Craig Gilroy, centre Gordon D'Arcy, flanker Stephen Ferris and fly-half Jonathan Sexton.
Head coach Declan Kidney, however, refused to complain about Ireland's misfortune.
"We took a conscious decision that we wouldn't complain about things. Other people are worse off than we are, plus it's such an insult to the lads coming on and having a huge go," Kidney said.
"We're frustrated, but there are lads coming in who have no experience at this level under their belts and are doing such a good job for us.
"On any given day Paul O'Connell, Tommy Bowe, Stephen Ferris and Jonathan Sexton would be in the running for a Lions spot.
"I've never experienced an injury run like this, but you work your way through and I spoke to (captain) Jamie Heaslip about it and we agreed not complain."
