Van Hoof was men's technical director at the 2016 Rio de Janeiro Olympics, where Britain's male gymnasts won five medals, including two golds for Max Whitlock. He was subsequently named UK Coach of the Year.
No details were given about the allegations.
"British Gymnastics confirms that an independent investigation is being conducted into allegations of misconduct relating to Eddie Van Hoof, pending the outcome of which he has been suspended," a statement said on Monday.
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"The suspension is not a disciplinary penalty, and indeed does not imply any assumption of guilt."
Reuters was unable to contact van Hoof.
(Reporting by Alan Baldwin; Editing by Kevin Liffey)
