Stevens, who damaged his rotator cuff in England's win against the Barbarians on Sunday, has been replaced in the touring party by Gloucester's Rupert Harden.
England head coach Stuart Lancaster said: "Firstly, it's really tough on Matt but he has been assessed by the medics and he wouldn't be able to train or play for some time.
"We wish him all the best but it's a great opportunity for Rupert, who has been the first-choice tight head for Gloucester this season and also involved in the Saxons during the Six Nations."
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The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
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