Both players have been hampered by knee problems, which are set to require further assessment.
Britton and Emnes are therefore expected to play no part when Swansea kick off the 2014-15 campaign with a visit to Manchester United on August 16.
A brief statement from Swansea on Sunday revealed the nature of the injuries.
It read: "Britton is suffering from a badly bruised bone in his knee, while Emnes has a meniscal (cartilage) problem.
"Both players will have another scan in two weeks' time to assess the full damage."
Britton, who has spent more than a decade at Swansea and represented the club in all four divisions of English football, made 34 appearances last term, while Emnes featured nine times after rejoining the club from Middlesbrough in January.
