The Rugby Football Union also confirmed that Karl Dickson of Harlequins will join the squad as a replacement.
The news is a huge blow for Youngs, who impressed by scoring two tries in Saturday's 36-27 second Test defeat in Johannesburg.
The 22-year-old Leicester half-back's performance was one of the key factors in England's revival after they fell 28-10 behind early in the second half.
He was withdrawn six minutes from time and replaced by Lee Dickson - Karl's brother - but England gave no indication that he had damaged his right shoulder after the game.
Lee Dickson may now be in pole position to start next Saturday's third Test in Port Elizabeth but Youngs' withdrawal could also offer an opportunity for Danny Care to resurrect his international career.
Care was dropped for the RBS 6 Nations by head coach Stuart Lancaster earlier this year after a series of off-field incidents.
The 25-year-old impressed in an England XV's victory over a Southern Barbarians side in Kimberley last week and could now be ready for elevation to the senior side.
Care's Quins team-mate Karl Dickson, 29, is due to fly Johannesburg overnight and will immediately be in consideration for Tuesday's tour match against the Northern Barbarians in Potchefstroom.
He has been summoned a day after Jonny May of Gloucester was called up to replace injured Harlequins wing George Lowe in the squad.
Bath's Nick Abendanon last week arrived after injury to Quins full-back Mike Brown while London Irish flanker Jamie Gibson replaced London Wasps' Joe Launchbury before the first Test.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
