The 41-year-old, who began his playing career at Stade Louis II, left his role as Belgium assistant in mid-October to take over at the Ligue 1 club following the sacking of Leonardo Jardim, but he is yet to oversee a win.
The 2016/17 French champions have lost three and drawn two of his first five matches in charge after a 4-0 home defeat to Club Brugge in the Champions League on Tuesday night.
Reviving Monaco's fortunes might be a bigger job than Henry anticipated.
Henry inherited a team that had won just one of their opening 12 games in all competitions under Jardim, losing eight of them. His first game in charge was a 2-1 defeat at Strasbourg, before he halted a five-match losing run with draws against Club Brugge and Dijon.
It looked like Henry had stopped the rot but another loss at Stade Reims followed at the weekend before overseeing an unwanted club record against Club Brugge on Tuesday night – Monaco's heaviest home defeat in the European Cup.
After the final whistle against Stade Reims, Henry and his players made their way over to the away end to show their appreciation for their fans support. However, the feeling was not mutual and there were ugly scenes as Monaco supporters rushed forward towards the front barriers to confront him and his team.
A flare was set off and thrown on to the pitch before stewards eventually intervened to calm the group down.
Henry has already criticised his players
It looks like Henry shares the concerns of the fans as – after the defeat at Stade Reims – he questioned the desire of the players, telling reporters at the post-match press conference: "When you enter the pitch and your players involuntarily refuse to play, it is difficult. We have to find our confidence again."
Then after the defeat to Club Brugge, Henry questioned Monaco's mentality. He told reporters at the post-match press conference: "I am upset with the way we reacted to falling behind. We started well, but once we fell behind we stopped playing and that's a little bit worrying."
And things could get worse
Monaco are without a win in their last 15 games in all competitions – their worst streak since the period from September 1968 to January 1969. They have amassed just seven points from 12 matches in Ligue 1 this season – the club's lowest tally at this stage in their top-flight history after the 1953/54 campaign.
The last thing Monaco need on this sort of run is a visit from free-scoring, high-flying Paris St Germain. The Ligue 1 leaders have won their first 12 games in the league this season to record the best-ever start for a team in the top five European Leagues.