The 32-year-old, who holds the Cumbrians' record for most appearances for an outfield player, has missed the last two matches and will be sidelined for another four to six weeks.
Danny Livesey and Mike Edwards have formed a partnership in central defence in Murphy's absence and are expected to continue in the FA Cup clash with Bournemouth on Saturday.
On-loan teenage pair Valentin Gjokaj (derby) and Sean McGinty (Manchester United) are also pushing for a place in manager Greg Abbott's starting line-up.
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- Danny Livesey