On February 17, 1979, Parent suffered a career-ending eye injury in a game against the New York Rangers. An errant stick entered the right eye hole of his mask, causing permanent damage to his vision. After hospitalization, including the complete loss of sight for two weeks, Parent recovered and eventually regained sight, although not at the level required to resume his playing career. He retired at age 34, an age considered to be "still in athletic prime" for goaltenders. This incident, as well as the ending of Gerry Desjardins' career when a puck struck his eye in 1977, led many NHL goalies to switch from fibreglass facemasks toward the cage and helmet style, and resulted in many amateur and junior leagues banning fibreglass masks altogether, mandating the helmet/cage combo.
After Parent's retirement the Flyers retired his jersey number (1) in his honor on October 11, 1979. He spent several years in the Flyers organization as goaltending coach, mentoring future Vezina-winning goalies Ron Hextall and the late Pelle Lindbergh, the latter of whom idolized Parent as a youngster in his native Sweden. Today, he is employed by the Flyers as Ambassador of Hockey. He can be seen at Flyers home games on the concourse.