The 29-year-old centre-half had minor knee surgery to repair cartilage damage on Friday and will play no part in the club's opening League One clash at Swindon on August 9.
Iron boss Russ Wilcox had been hoping Mirfin's problem was not too serious, but the former Huddersfield and Watford centre-half will be sidelined for a month.
Winger Terry Hawkridge, meanwhile, will sit out Saturday's friendly at his former club Gainsborough Trinity due to a knee problem.
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