The 30-year-old went down to Belgian Zizou Bergs in the second round.
India's highest-ranked men's singles player Ramkumar Ramanathan and Sumit Nagal could not cross the first hurdle.
With both Bhambri and Ramanathan bowing out, Sania Mirza, who is in her last year on tour, remains the only Indian confirmed to play at Wimbledon this year.
Yuki Bhambri and Ramkumar Ramanathan posted comfortable wins on the opening day.
Ramkumar Ramanathan will play for Mumbai Leon Army. He was picked up for Rs 4.5 lakh.