The 23-year-old started the first two games - a loss to Ireland and a win against France - but dropped out of the squad for last weekend's 16-15 Calcutta Cup victory over Scotland due to fitness concerns.
He has now been told he will not be fit to face Italy on March 9th or Wales the following week.
"Unfortunately, he won't play any further part in the Six Nations for us," Kevin Sinfield, England's skills and kicking coach, said Thursday of Martin's injuries.
"He's actually got two - the knee, which has been a niggle for some time, and the shoulder as well. It will be the shoulder that will keep him out.
"We're very hopeful it won't be long after the Six Nations but there's still some medics investigating further."
England are third in the Six Nations table with two games to go, a point behind France and four behind unbeaten defending champions Ireland.