Kerber, the three-time Grand Slam and reigning Wimbledon champion from Germany, was stunned by world number 81 Anastasia Potapova of Russia, 4-6, 2-6.
Venus, the seven-time Grand Slam winner from the US, was beaten by Ukrainian ninth seed Elina Svitolina, 3-6, 3-6.
The only Indian in the Singles, Prajnesh Gunneswaran, playing in his first Grand Slam, also bowed out after losing to Marco Dellien of Bolivia, 1-6, 3-6, 1-6.
Second seed Karolina Pliskova, third-placed Roger Federer, Stefanos Tsitsipas, Kei Nishikori and Sloane Stephens advanced to the Singles second round.
World number one Novak Djokovic, second seed Rafael Nadal and 23-time Grand Slam winner Serena Williams are among those who will begin their campaigns on Monday.