The 22-year-old Greek won his last title in February last year at the Open 13 indoor tournament in Marseille - just weeks before France went into lockdown.
Djokovic, the Monte Carlo champion in 2013 and 2015, was broken five times by the 33rd-ranked Evans and suffered his first loss of the year.
Second-ranked Daniil Medvedev withdrew from the Monte Carlo Masters on Tuesday following a positive COVID-19 test.
The 21-year-old displaced Marin Cilic after his progress to the Monte Carlo Masters semi-finals won on Sunday for the 11th time by Nadal.
The 31-year-old saw off Nishikori 6-3, 6-2 to become the first man to win a single tournament 11 times in the Open era with his 76th ATP Tour title.
Three-time Grand Slam champion Murray had hip surgery in Melbourne at the start of the year and is targeting a return for the grasscourt season.
Rafael Nadal crushed fifth seed Dominic Thiem 6-0, 6-2 to romp into the Monte Carlo Masters semi-finals on Friday.
The top-seeded Spaniard, who claimed his 10th Monte Carlo title last year, has a bye for the first round.
Rafael Nadal won eight Monte Carlo titles in a row from 2005 to 2012 but then lost to Novak Djokovic in the 2013 final.