Authorities intend to look into Gradi's involvement in the historic child sex abuse scandal that has rocked football.
Crewe has been at the centre of the shocking allegations, with numerous ex-players claiming that they suffered abuse at the hands of former coach and convicted paedophile Barry Bennell.
It is unclear whether his suspension is in relation to alleged crimes that occurred at Crewe or over allegations that while working as Chelsea assistant coach he visited the home of a former youth player to help 'smooth over' a complaint of alleged sexual assault against Eddie Heath.
On Monday, Crewe released a statement, which read: "Following discussions with the Football Association, Crewe Alexandra Football Club can confirm that Dario Gradi is currently under an FA interim suspension from football."
The 75-year-old denies any wrongdoing and will cooperate the FA's review.