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The 23-year-old completed the match at Goodison Park, but went down holding his shoulder late on, and subsequently required further assessment from the Red Devilsmedical staff.
He was forced to sit out England's 3-0 friendly victory over the Republic of Ireland on Thursday night, with Jack Grealish, Dominic Calvert-Lewin and Jadon Sancho making up Southgate's front three in his absence.
English football's main governing body also confirmed that Wolves defender Conor Coady has pulled out of the squadin accordance with Covid-19 regulations, and must now undertake a period in quarantine.
"Conor Coady and Marcus Rashford will miss England’s remaining November internationals. Coady has been forced to self-isolate having discovered he had inadvertently come into contact with somebody prior to camp who has tested positive for Covid-19 via an NHS Test and Trace alert," an official statement from the FA reads.
"The Wolverhampton Wanderers defender had returned two negative tests as part of The FA and UEFA’s protocol but, in line with UK Government guidelines, has to adhere to a period of self-isolation.
"Meanwhile, Rashford’s arrival into camp had initially been delayed to allow for further assessment on an injury sustained last weekend but the Manchester United forward will now not meet up.”
United fans will hope that Rashford will benefit from an extra week of recovery time with a view to returning to action when Ole Gunnar Solskjaer's men play host to West Brom on November 21.
The England forward has scored seven goals in 12 appearances for the Red Devils in all competitions this season, while his last goal for England came from the penalty spot in a 2-1 win over Belgium on October 11.