The Stade Louis II club announced on Thursday that they had suspended Henry ahead of a "final decision" on his future, but it is understood he has already left the club.
Henry began his playing career at Monaco and was handed his first managerial role by the club in October as he left his role as Belgium assistant boss to replace Leonardo Jardim.
Assistant coach Franck Passi will take training on Friday and Jardim is expected to return to replace Henry.
Monaco won just five games in all competitions under Henry and failed to win any of their Ligue 1 matches at the Stade Louis II under the French World Cup winner.
The 2016-17 French champions currently sit 19th in the Ligue 1 table and three points adrift of safety ahead of Saturday's trip to relegation rivals Dijon.