Morgan picked up an ankle knock in the opening-day win over Scotland and has been ruled out of the clash with France this Saturday.
However, coach Lancaster has insisted that there is no long-term damage and is hopeful that the Gloucester number eight will return for the March 10 fixture against Italy.
"Ben will be fine," Lancaster said. "It's similar to the one Manu Tuilagi was out for four or five weeks with and Ben will be about the same.
"He wants to get himself right so he can push for selection against Italy."
Morgan has been capped 10 times since debuting for England in 2012.