Southgate has a thigh injury and will be replaced in the squad by a first senior call-up for Anthony Gardner of Tottenham Hotspur, the Football Association said on Tuesday.
Southgate was himself a stop-gap for the game at Old Trafford, his re-call on Monday being due to the unavailability of Sol Campbell and Jonathan Woodgate.
Beckham, who suffered a back injury in Real Madrid's 4-1
Having been advised by club doctors to rest until Wednesday, Beckham has been left out of Real's squad for a friendly against Valladolid on Tuesday.
England's medical staff will speak to their Everton counterparts on Wednesday about Rooney, who missed their defeat by Blackburn Rovers on Monday due to 'flu.