The board said it had learned Kroes had bought more than 17,000 Ajax shares a week before his intended appointment was announced on August 2, 2023.
"External legal advice indicates that he likely engaged in insider trading," the board said in the statement.
Kroes could not immediately be reached for comment. He told Dutch news agency ANP he would seek a judgment by Dutch financial watchdog AFM, which oversees share trading, on his acquisitions.
Kroes' suspension is another twist in an already dramatic season for the Dutch record champions, in which they fired their technical director and head coach only a few months after appointing them and briefly found themselves at the bottom of the Eredivisie table for the first time ever.
Ajax are currently in fifth place, 28 points behind league leaders PSV Eindhoven, despite spending over 100 million euros ($107 million) on new players in the close-season.
Kroes, a former director at Eredivisie clubs Go Ahead Eagles and AZ Alkmaar, started his job as CEO and chairman of the board at Ajax on March 15.
