That would mean the British & Irish Lions lock would probably not return until the final match against Scotland on March 16.
Itoje was on Monday afternoon due to see a specialist to be given a clearer picture of when England can expect him back.
"We anticipate him being able to play at the latter part of the tournament. I am a fully signed-up member of the low-key, respectful Schmidt approach every time and I qualify that by saying that what goes on behind closed doors at in-house meetings is very different to that dished out at PR-perfect press conferences for public consumption".
"I suppose in the warm-up, if you look at our back line, we are a bunch of quiet lads anyway".
Either Courtney Lawes or Joe Launchbury will slot into the starting XV in his absence, partnering George Kruis in the second row.
Itoje's Saracens team-mate Nick Isiekwe has been called into England's 35-man training squad ahead of Sunday's match against France at Twickenham. He said: "He's going to be the best lock in the world so it's a big loss.' While some reports have suggested that the 24-year-old will be sidelined for eight weeks, sources have indicated to Sportsmail that that would be the worst-case scenario".
He's a brilliant player and he's a world-class player.
Their performance was hardly befitting of the first match - at home to boot - since Schmidt, the team and playmaker Johnny Sexton won World Coach of the Year, Team of the Year and Player of the Year.
"We all saw the impact Lawes had off the bench, the hitting power he has and how he can carry. We always look at different combinations and we'll be doing that over the next few days".
England's dominance was epitomized by their pack, who won most of the physical encounters and seized the forward momentum that enabled their ball carriers to run at the Ireland defense, such as when Manu Tuilagi powered through Josh van de Flier to start the move that led to Jonny May's opening try.
Meanwhile, two days after helping England record the greatest victory of the Jones era, Mark Wilson was brought down to earth through a shift of changing nappies.
But after an impressive win against France in Paris, Wales will surely have silverware ambitions of their own going into the monumental clash with England in Cardiff on February 23rd in what is essentially a title decider. "I absolutely hate it", Ward said on the BBC Sport website.