The club, who have won only two league games under Henry and are second from bottom of Ligue 1, said a final decision would be taken on the former striker’s future and that Franck Passi would train the first team on Friday.
Henry has been in charge for 104 days. Monaco lost to the League 2 side Metz in the French Cup on Tuesday, having been beaten 5-1 at home by Strasbourg in the league last Saturday.
Henry had talked bullishly earlier on Thursday, saying his team were “going to war” in Saturday’s game against Dijon after five matches without a win.
“We need guys who want to save the club, who don’t think about themselves,” Henry said. Asked who would be left out at Dijon, he replied: “You will see. There are too many names …”
Monaco gave Henry, one of their former players, his first job as a manager after he had worked as an assistant to Roberto Martínez with Belgium, including at the World Cup.