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England's selectors also chose to rest off-spinner Graeme Swann, a regular in all three international formats, following their 3-2 one-day series win over Australia completed at Lord's here yesterday where batsman Pietersen suffered his injury during a 42-run loss.
Jonathan Trott, like Pietersen born in South Africa, was called up into the squad, with off-spinner James Tredwell taking Swann's place in two like for like replacements.
Pietersen, who has now gone 16 innings without a one-day fifty after falling for a duck at Lord's, injured himself while fielding and is now due to undergo further assessment of the quadriceps strain in his left leg.
Swann meanwhile will be able to play County Championship cricket for Nottinghamshire to help him prepare for England's four-Test series against Pakistan starting in July.
Left-arm quick Ryan Sidebottom was left out of a 13-man squad after not featuring against Australia in a series where England fielded the same XI in all five matches.
England national selector Geoff Miller said: "It's unfortunate Kevin Pietersen has suffered an injury – and although we'll know the full extent in due course, it looks like he'll be able to make a full recovery very quickly.
"Graeme Swann has been involved in all forms of the game for some time now, and this forthcoming period has been identified as the best opportunity to ensure he has a suitable
break before a demanding schedule this summer and during the winter."
Former England off-spinner Miller added: "James Tredwell and Jonathan Trott have previously been involved with the England one-day set-up and will be excellent additions to the full England squad from the England Lions.
"Both have been in good form for the Lions and will relish the opportunity to make their mark in limited overs at the top level."
England, who were 3-0 up, may have lost their last two one-dayers against world champions Australia by convincing margins - they were beaten by 78 runs at The Oval on Wednesday - but Miller said the side could take heart from a series win.
"There was a lot to like about the cricket we played against Australia, and the team will be looking to build on this against Bangladesh."
England's three-match ODI series against Bangladesh starts at Trent Bridge on Thursday.
Andrew Strauss (capt), James Anderson, Ian Bell, Tim Bresnan, Stuart Broad, Paul Collingwood, Craig Kieswetter (wkt), Eoin Morgan, Ajmal Shahzad, James Tredwell, Jonathan Trott, Luke Wright, Michael Yardy.