The British number one was well on the way to the landmark victory, leading 6-2 3-0, when her compatriot withdrew after suffering a left foot injury.
Konta was bossing matters in the first-round tie with her consistency, taking the first set with two breaks of the 24-year-old's serve.
It was three games without reply for Konta in the second set when British number four Moore called it a day.
Konta, top seed in Nottingham, was then presented with a celebratory bunch of flowers on court after the match to celebrate the milestone victory.
She now faces Belgian Yanina Wickmayer in the second round.