It had been reported in the Dutch media that the legendary former Netherlands striker had been suffering from heart palpitations following the death of his father in July.
The problem forced him to miss Saturday's Eredivisie clash at Dordrecht, and he has now been given leave until September 14 - after AZ's next league fixture against Heerenveen.
"As a club we know our responsibilities", said director of football affairs Earnest Stewart.
"On the advice of our club doctor and in consultation with Marco we have decided that resting will accelerate the recovery.
"Football is very important, but good health is paramount."
Van Basten, 49, was confirmed as Dick Advocaat's successor at AFAS Stadion in April.
Dennis Her and Alex Pastoor will continue to manage first-team affairs in his absence.
