The claim that Obama is standing in front of a Muslim prayer curtain is false. This meme has gone really viral and has been debunked on over 10 websites online. The picture that you see is taken in the East Room.
The East Room, designed for "public audience", is an events and reception room in the White House, the home of the President of the United States.
What you see behind Obama is simply:
gold silk lampas curtains
It is reported that those gold silk lampas curtains have been in the East Room since the John F. Kennedy administration.
They were designed by noted ballet and theatrical designer Jo Mielziner:
Mielziner crafted a stage which took up a full third of the East Room, and featured cream white-painted pilasters matching the room's architecture. Mileziner originally wanted the stage's curtains to have the same fabric used for the East Room drapes. But when he learned of the cost, he settled for American-made gold silk curtains instead. The larger stage took eight men three days to set up. (1)
In September 2003, during the administration of George W. Bush, minor refurbishment were made to the East Room, and gold silks were replaced:
The Committee for the Preservation of the White House had become dissatisfied with the golden silk swag valances installed during the Reagan presidency. The Kennedy-era Old World Weavers Empire-style gold draperies were replaced with nearly identical ones, but the swags were made 12 inches (30 cm) deeper to make them appear more substantial. The room was repainted in the same warm cream color it had for the last century. The refurbishment cost $200,000, and was paid for by private donations to the White House Endowment Fund. (2)
Here is a photo of Lyndon B. Johnson's daughter, Lynda Johnson, wedding in the East Room (source: celebritybrideguide.com) back in 1967. Note the gold curtains in the background:
Another picture of Gerald Ford, the 38th U.S. President, being sworm as a president in 1974, also clearly shows gold curtains:
Also, a picture of Bush standing in front of a gold silk:
Reddit responded to the meme in its own way (with another meme):
Additionally, according to members of islam.se, there is no such thing as a Muslim prayer curtain.
So, the claim that President Obama has a so-called a Muslim prayer curtain is not only erroneous but ridiculous too.
(1) West, J.B.; Kotz, Mary Lynn (1973). Upstairs at the White House: My Life With the First Ladies. New York: Coward, McCann & Geoghegan. ISBN 069810546X.
(2) Koncius, Jura (September 25, 2003). "Open Door Policy At the White House". The Washington Post.