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The ECB said it will not call up a replacement and Leach will head home from Abu Dhabi.
Leach didn't take part in the team's training session on Wednesday and was seen receiving treatment from the physio on the sidelines.
Leach, 30, landed awkwardly on his head while trying to prevent a boundary.
There is a good chance that pacer Mark Woods will return to the playing eleven in place of James Anderson, who could be rested after featuring in four games.
'I don't want to see the crowd talking about how funny he is. I want to see him winning matches for England with his bowling,' Kevin Pietersen said.
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