World number two Zverev has struggled for any kind of form since his defeat by Jannik Sinner in the Australian Open final at the end of January, winning just six of 12 matches.
But with a first-round bye in the absence of world number one Sinner, who is suspended for a doping violation until May 4, Zverev was among the favourites.
After a controlled start to the game, the German slumped to a 2-6, 6-3, 7-5 defeat to 34th-ranked Berrettini, at the end of a high-flying match, which had included an impressive 48-stroke rally won by the Italian.
“It’s been the worst period since my injury [the] last few months,” said Zverev who has suffered a string of early exits of late, including at Indian Wells.
“I played a great first set, and once I got broken in the second set I play ten levels down. My ball is much slower. I stopped hitting the ball.
“The same story the last few months. Nothing changes. So it’s me who lost the match, once again.
“I thought my level was terrible, but that’s just my opinion.”
Defending champion and three-time Monte Carlo winner Tsitsipas advanced past 38th-ranked Australian Jordan Thompson.
After a lacklustre US tour, the Dubai winner won through 4-6, 6-4, 6-2 in his second round tie.
Indian Wells champion Draper, seeded fifth, eased past 45th-ranked American Marcos Giron 6-1, 6-1.
Novak Djokovic – the winner in 2013 and 2015 – and Carlos Alcaraz start their campaigns on Wednesday. (AFP)
