The decision means the South African-born number three, whose future with England had already been called into question, can be ruled out of the test series against Pakistan between July 14 and Sept. 7.
Durham's Scott Borthwick looks likely to be recalled for the opening test at Lord's.
"It has been agreed that the best way forward is for Compton to spend some time away from the game," Middlesex said in a statement, which did not indicate how long the break might be.
The county side's managing director of cricket, Angus Fraser, said it would allow him to "refresh, recharge and return to play the sort of cricket we all know he is capable of producing."
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The statement added that the player, who turns 33 on Sunday, would receive the full support of his county and England management.
Compton, has been suffering a run drought and scored only 51 from five innings in England's recent test series against Sri Lanka.
Former England captain Mike Atherton said earlier this month that Compton 'just hadn't got going' and expected him to be dropped for the Pakistan series.
Fraser told Sky Sports television at Lord's that the player was tired: "He's not where he wants to be at this moment in time. He's obviously disappointed with the way things went.
"We haven't put a date on it," he said of the player's eventual return. "We'll see how he goes and monitor it and when Nick's ready, I'm sure he'll make contact with us and get back into training.
"He's frustrated by what's taken place and trying to work it all out and make some sense of it. I'm sure he'll be back and keen to carry on his career."
The grandson of England great Denis Compton said last month that he felt his England career was on the line.
"I want to feel good about my batting and I want to feel good about contributing to the England team," said Compton, who has played 16 tests, with an average of 28.70 runs.
"Those are my driving motivations. If you don't play well enough you get dropped. That's fundamentally how it works."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
