Third in the 500 earlier in the day, Kodaira, who won the 500-, 1,000- and 1,500-meter crowns at last month's single-distance national championships, clocked 1 minute, 15.92 seconds to finish behind Christine Nesbitt of Canada.
Nesbitt won the gold in 1:15.41, Dutchwoman Marianne Timmer took third place in 1:16.13, while Japan's Sayuri Yoshii (1:17.34) and Tomomi Okazaki (1:18.07) placed 10th and 17th, respectively.
China's Wang Beixing claimed victory in the 500 in 37.85, with German's Jenny Wolf finishing 0.19 second back. Kodaira timed 38.19.