The defeat was the Ligue 1 side's heaviest in the competition and leaves them with one point from four matches.
Henry, 41, is winless in five games in charge, with this a third defeat.
A Hans Vanaken double and a Wesley Moraes strike put Club Brugge 3-0 up at the break, before Ruud Vormer completed the victory late in the second half.
The loss extends Monaco's run this season to 15 games without a victory in all competitions - they have not won since their second game of the campaign.
Atletico Madrid's 2-0 victory against Borussia Dortmund in Spain means those two teams have nine points in Group A, while third-placed Club Brugge have four points and retain an outside chance of reaching the knockout stages.
MonacoClub Brugge
- Possession
- 65%
- 35%
- Shots
- 15
- 7
- Shots on Target
- 6
- 6
- Corners
- 6
- 1
- Fouls
- 16
- 13
Tags:
Uefa Champions Legue