However, they are expected to be fit for the upcoming tour of Bangladesh.
Anderson, England's all-time leading wicket-taker, requires what an ECB statement said was "ongoing rehabilitation" of his right shoulder and won't now feature again for Lancashire in the remainder of the 2016 county season.
Broad, who last played for Nottinghamshire in their Twenty20 Blast semi-final defeat by Northamptonshire at Edgbaston last Saturday, is recovering from an ankle problem.
"Both players have managed their injuries through the summer and a break from cricket is needed to best prepare the Test opening bowling pair for England's winter campaign that begins this October in Bangladesh," the ECB statement added.
Anderson and Broad were both omitted from England's squad for their ongoing five-match one-day series against Pakistan, with the duo now regarded as Test specialists by the England management.
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