Worcestershire paceman Brown suffered a recurrence of lower back issues while preparing to play for the Melbourne Stars in the Big Bash League.
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Scans revealed a partial stress fracture and the 21-year-old has withdrawn from all cricket for the time being.
Brown will return to England to begin his rehabilitation with his county.
The ECB added England will confirm a replacement for the three-match ODI series, which starts on February 4, and the three T20s to follow.
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