Sindhu was off to a sluggish start, slipping to 1-6 before settling into rhythm and cutting the deficit to 5-9. But An dictated the rallies, going into the interval with an 11-5 cushion.
The six-day China Masters was due to start on February 25 at Lingshui, in China's southern Hainan island.
Sindhu will square off against Indonesia's Dinar Dyah Ayustine in the opening round.
Kashyap lost 10-21 22-20 13-21 to former World No. 6 and third seed Qiao Bin of China.
Kashyap defeated Thailand's Suppanyu Avihingsanon 21-16, 21-17 to progress to the pre-quarterfinals.
