Twenty-eight men's opening-round matches were either suspended or postponed because of rain, including one involving world No. 1 Roger Federer.
Rain also disrupted Sunday's opening-day schedule.
Davydenko defeated Italian Stefano Galvani, 6-3, 6-1, 6-1, in 90 minutes. The Russian star broke serve seven times.
Federer -- the top-seed and 2006 French Open runner-up -- was leading American Michael Russell, 6-4, 4-1, when their match was suspended until Tuesday.
Federer is the reigning Wimbledon, U.S. Open and Australian Open champion. He needs a French Open title to complete a career Grand Slam.
Rain is in the forecast for Tuesday.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
'Happy' fan videos make Pharrell cry [VIDEO]