The world number two, who is the top seed at the tournament, beat Andrey Golubev in straight sets, allowing his opponent to win just five games.
The Serb told BBC Sport: "It was a great start, especially in the first two sets. Credit to Andrey for coming back in the third, but I cannot be happier with the performance.
"It's never easy coming into a tournament, and you can never underestimate any opponents. But I started extremely well and played a very good game.
"I don't know why somebody would have concern about my physical condition, I had two weeks off after the French Open, and that's more than enough time to get ready for a grass court tournament."
Djokovic faces Radek Stepanek in the second round.