The Saracens lock was taken off in the second half of England's 32-20 victory over Ireland at the Aviva Stadium on Saturday.
"We anticipate him being able to play at the latter part of the tournament".
Either Courtney Lawes or Joe Launchbury will slot into the starting XV in his absence, partnering George Kruis in the second row.
Wasps second row Joe Launchbury is favourite to be called into the matchday squad for England's game against France at Twickenham on Sunday, 10 February.
"He's a brilliant player and he's a world-class player", England scrumhalf Danny Care, who was not named in Eddie Jones' squad, told BBC's Rugby Union Weekly.
"Maro's going to be the best lock in the world so it's a big loss, but we've got good depth", Jones said.
Itoje was on Monday afternoon due to see a specialist to be given a clearer picture of when England can expect him back.
Itoje unknowingly chipped his right kneecap in training in November before England's last global that month against Australia.
He was ruled out for five weeks after suffering a chipped patella to the same knee in the build-up to the autumn series, playing throughout November until the nature of the injury was discovered.
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