Already without one British and Irish Lion after centre Robbie Henshaw was ruled out for the rest of the championship, prop Furlong and lock Henderson failed to recover in time from knocks picked up in the 56-19 thrashing of Italy two weeks ago.
Ryan, an impressive Six Nations debutant against France, returns at lock while his Leinster team mate Andrew Porter, one year his senior at 22, comes in for Furlong. Munster's Chris Farrell, 24, makes his championship debut in place of Henshaw.
"Yes, we're short on experience and we're up against a team welcoming back three Lions while we see three disappear, that's not ideal," Schmidt told a news conference in reference to the return of Dan Biggar, Leigh Halfpenny and Liam Williams for Wales.
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"You suddenly have to replace world class players but we're more focussed on who we do have - and who we do have is Andrew Porter who is a really promising young player that we're excited about. James Ryan, likewise. Chris Farrell has been a long term project and I thought he did really well against Argentina in only his second test."
While the new men have just 11 caps between them, Farrell showed signs of striking up a comfortable partnership with Bundee Aki against Argentina in November and Porter made a big impression after replacing Furlong early on against Italy.
Cian Healy, who returns to the pack alongside CJ Stander in the only other change, was excited about the impact the younger players could make up front.
"Over the last year and a half with what he's had to take in his stride, changing sides on the scrum and how he's developed that part of his game, it's more exciting than nervous to see what he's going to provide. He's a very talented player," Healy said about his fellow Leinster prop Porter.
"And then there's the freak show that is James Ryan, he keeps producing and that's exciting as well, to have his energy behind you in the scrum is brilliant."
Team
15-Rob Kearney, 14-Keith Earls, 13-Chris Farrell, 12-Bundee Aki, 11-Jacob Stockdale, 10-Johnny Sexton, 9-Conor Murray; 8-CJ Stander, 7-Dan Leavy, 6-Peter O'Mahony, 5-Devin Toner, 4-James Ryan, 3-Andrew Porter, 2-Rory Best (captain), 1-Cian Healy.
Replacements: 16-Sean Cronin, 17-Jack McGrath, 18-John Ryan, 19-Quinn Roux, 20-Jack Conan, 21-Kieran Marmion, 22-Joey Carbery, 23-Fergus McFadden.
(Reporting by Padraic Halpin; Editing by Toby Davis)
