The Gloucester No8 picked up an injury during the tournament’s opening fixture against Scotland at Twickenham and has been missing since.
There was better news for Lancaster though after it was announced second-row trio Courtney Lawes, Joe Launchbury and Geoff Parling will all be fit for the weekend, while Farrell, who missed England’s narrow 18-11 win against Italy, will also be available.
“Ben will stay at Gloucester this week. We knew his ankle would take six to eight weeks and he won’t make it in time,” said Lancaster.
“We’re going to miss Ben, which is disappointing for him having worked so hard to be fit.
“With a six-day turnaround you’re not going to make a huge number of changes at this point of the championship.
“We’re hopeful [over Launchbury, Parling and Lawes] but we’re not definite at this point so we’ll see how that goes.
“We’ve got Owen Farrell back in the equation, which is pleasing, and we’ve got other lads who have been waiting patiently.
“We’ll make those decisions in the next 24 hours. We’ve only got one training session before we announce the team on Thursday and head to Cardiff.”