Klose, who resumed playing in October after a month-long injury break, picked up a shoulder injury in Lazio's 1-1 draw at Parma in Serie A on Sunday.
"The current situation is Miro Klose will not be able to play in the two games," Germany coach Joachim Loew told reporters on Wednesday. "He injured his shoulder and will be out for two or three weeks."
"Per Mertesacker will remain in London and will join us when we are there for the game (on Tuesday)," he said of the Arsenal central defender.
Mertesacker's club mate Mesut Ozil, who has had a flu virus, has been passed fit for both friendlies, Loew said.
Loew assured Klose and his fellow injured forward Mario Gomez they remained his first choice for Germany, who have qualified for the 2014 World Cup in Brazil, if injuries did not upset their rhythm early next year.
"It is part of our job to build up players who can fill gaps," said Loew, who will coach his 100th international on Friday, becoming only the fourth Germany manager to reach a century.
He said Borussia Moenchengladbach's Max Kruse and Bayern Munich's Mario Goetze are his favoured strikers to cover a shortage up front.
"Obviously, it is a pity that Mario and Miro are out but I do not see a problem. For me, January is the cut-off date. If a player starts the new year normally after completing winter training and then plays through then I am certain he will join us in good form."
Loew said his players would not be seeking revenge against Italy for their Euro 2012 semi-final defeat but he still expected them to show full commitment despite the distraction of next week's top-of-the-table Bundesliga clash between Bayern Munich and Borussia Dortmund.
"I don't think the players are thinking about it yet," he said. "I have always tried to consider clubs in my decisions but I do not want anyone to come to me and tell me to rest them on Friday or Tuesday."
"I have told them there are not many games left until the World Cup. If someone thinks they are automatically picked then they are wrong. I demand full speed ahead from everyone. We've got a high level squad and there are no free passes to Brazil."
(Reporting by Karolos Grohmann; editing by Amlan Chakraborty and Ken Ferris)
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