Mahesh - ranked 65 - trailed his rival, ranked 35th on the professional squash circuit, by two games and was down 3-5 in the third when he retired hurt after 20 minutes on court at the Cricket Club of India (CCI) here.
Mahesh had come through the qualifying rounds.
Top seed Fares Dessouky of Egypt, ranked 18th in the world, led the other seeds into round two with a clinically efficient 3-0 victory in 37 minutes over Olli Tuominen of Finland.
Later, India's multiple-time national champion Saurav Ghosal recovered from the loss of the first game to put it across Malaysian qualifier Ivan Yuen 3-1.
The tournament's fourth seed, ranked 23rd currently globally, subdued his Malaysian rival 7-11, 11-2, 11-6, 11-8 in the best-of-five encounter in 69 minutes to enter round two. Ghosal will meet Swiss Mueller in the quarter finals.