The experienced pace bowler had scans on a bruised left heel after bowling only one over for Nottinghamshire in Leicestershire's second innings as his side defeated their Midlands rivals in the Second Division of the County Championship this week.
But with scans inconclusive, England hope the old-fashioned approach of a week's rest will help the 30-year-old Broad regain full fitness in time for the first of a four-Test series that starts on July 6.
He will now miss the four-day Championship match against Kent starting on Monday.
An England spokesman added it was not yet clear if he would be fit to play for Nottinghamshire in their One-Day Cup final against Surrey at Lord's on July 1, but said he would "hope to be fit" for the first Test at the 'home of cricket'.
Nottinghamshire coach Peter Moores said: "Stuart has been assessed by the medics over the last 24 hours.
"They have ruled him out of the Kent game for him to keep getting treatment, and then we'll wait to see how he responds to that treatment."
Broad, who no longer plays white-ball cricket for England, had taken 16 wickets at 20.87 in five Championship matches so far this season. He has also taken 10 wickets in as many One-Day Cup games en route to the final.
If Broad, a mainstay of England's Test attack with 368 wickets in 102 matches, plays in the final without suffering any adverse reaction, he will likely be named in the first Test squad.
That would be a relief to England given the fitness problems affecting several of their other seamers.
James Anderson, Broad's longstanding new-ball partner and England's all-time leading Test wicket-taker, has only recently returned from a groin injury, Chris Woakes is struggling with a side strain and all-rounder Ben Stokes has been hampered by a knee problem.
First Published: June 24, 2017, 10:56 AM IST