Winterstein, who has signed a contract with Bradford for the 2014 Super League season, underwent surgery on Friday to re-attach his pectoral muscle after tearing it from the bone during Samoa's 42-24 defeat by New Zealand last Sunday.
The 14 competing nations submitted their final 24-man squads last month and, according to competition rules, any requests to make changes after October 21 are at the discretion of tournament organisers and will be only granted in exceptional circumstances.
A statement said: "Samoa recently approached RLWC2013 to change two players in their squad. After due consideration the request was denied."
A spokesperson for Samoa said they had accepted the ruling and will operate with a 23-man squad for the rest of the tournament.
They will be without captain Harrison Hansen, the Wigan second rower who is still recovering from a leg injury sustained in Samoa's friendly against England Knights, and stand-off Reni Maitua, who was hurt in the defeat by the Kiwis, for Monday's second Group B match against Papua New Guinea in Hull.
Samoa coach Matt Parish has been able to name only 18 players in his squad, which will be led by St Helens second rower Sia Soliola for the second time.