The Frenchman, seeded sixth, went down tamely 6-2 6-3 to Russian Andrey Rublev.
Eighth seed Andreas Seppi of Italy beat another Frenchman, Jeremy Chardy, 7-5 2-6 6-4, and Spain’s Guillermo Garcia-Lopez beat Denis Kudla of the United States 7-5 6-4.
Kyrgios hints at retirement after being beaten twice at Laver Cup as Team Europe sweep Day Two
There were mixed results for the Australians on home turf with John Millman beating American Frances Tiafoe 4-6 7-6 (7/5) 7-5, but James Duckworth bowed out 3-6 6-3 6-4 to Hungary’s Marton Fucsovics.
At the ASB Classic in Auckland, David Ferrer’s farewell tour continued with a routine win over Robin Haase.
The 36-year-old Spaniard, who will retire in May, beat Dutchman Haase 6-2 6-1.
Germany’s Peter Gojowczyk edged past Guido Pella of Argentina 6-1 3-6 6-2 and Leonardo Mayer, also from Argentina, beat America’s Steve Johnson 7-5 6-3.
'Utterly ridiculous tennis!' - Rublev wins incredible point in shock loss to Struff
ATP Monte Carlo
Tsitsipas happy to follow mother onto Monte Carlo honour roll