Radwanska was trailing 0-6, 1-2 in the second set against the 22-year-old Govortsova when she pulled out of the match, sending her Belarusian opponent into the round of 16.
Govortsova will face seventh-seeded Maria Kirilenko, who advanced with a Monday victory over Israel's Shahar Peer.
Also moving into the third round Tuesday was French Open runner-up Sara Errani, who dispatched Spaniard Carla Suarez Navarro 6-4, 6-3. The fourth-seeded Italian will meet fifth-seeded Marion Bartoli of France, who needed three sets to top American Sloane Stephens 6-1, 0-6, 6-3.
China's Zheng Jie downed Bulgarian Tsvetana Pironkova 7-5, 6-2 in another Day 3 match.
Celebrity Families of 2014 [PHOTOS]