The 52-year-old Frenchman reinforces a staff of first-time coaches with little Ligue 1 experience.
Henry, who is in his first management job, is rediscovering the French topflight, which he left in 1999.
Neither of his assistants has any experience in France.
Irishman Patrick Kwame Ampadu joined from Arsenal where he had spent six years coaching youth teams. Portuguese Joao Tralhao was a youth coach at Benfica.
On their web site, Monaco noted that Passi was familiar with both the French league and the role of assistant after working in that capacity under Marcelo Bielsa at Marseille and Lille.
Passi also worked under Elie Baup and Michel at Marseille. He had stints as head coach at Marseille and caretaker at Lille.
As a player, he spent the 1993-1994 season at Monaco and his brother Gerald is a scout for the club.
Monaco have won just three of 13 games in all competitions since Henry was appointed in October. They are 19th in the 20-team Ligue 1, three points away from safety.
Passi will be on the bench on Saturday when Monaco entertain the one team below them in the league, Guingamp.