Sharapova and Flipkens will be replaced in the 28-player draw by world number 46 Daniela Hantuchova and Christina McHale, who is ranked 79th.
Former world number one Ana Ivanovic eased into the second round of the China Open on Saturday, defeating American Christina McHale in straight sets 6-3, 6-2.
Canadian Aleksandra Wozniak snapped a 20-year drought by reaching the quarter-finals of the rain-plagued WTA Tour's Rogers Cup with a 7-6 (7/5), 6-3 win over American Christina McHale on Saturday.
Sixth-seeded Tomas Berdych lost in straight sets to Steve Darcis of Belgium on Saturday in the first round of Olympic play at Wimbledon while Christina McHale of the United States lost to Ana Ivanovic 6-4, 7-5 Saturday in the first round.
Injured Marion Bartoli will need to recover fitness when she plays American Christina McHale, who lined up a Friday quarter-final at the WTA event with a 4-6, 6-4, 6-4 win over Misaki Doi.
Defending champion Li Na of China shook off a tentative start to reach the French Open last 16 on Saturday with a 3-6, 6-2, 6-1 win over America's Christina McHale.
American teen Sloane Stephens advanced to the fourth round at the French Open by beating Mathilde Johansson of France 6-3, 6-2 on Friday.
Past and present Wimbledon winners Maria Sharapova and Czech Petra Kvitova made straight-set moves into the third round of the Rome Masters on Tuesday, with the Russian second seed made to work hard.
Serena Williams put the United States into a commanding 2-0 lead in the Fed Cup World Group play-off tie with Ukraine at Kharkiv on Saturday by beating Elina Svitolina in straight sets.
Spain's Anabel Medina Garrigues defeated qualifier Melanie Oudin 6-4, 4-6, 6-0 on Monday as the main draw action got underway at the WTA Tour's Charleston tournament.
Reigning Wimbledon champion and WTA Player of the Year Petra Kvitova exited Indian Wells when Christina McHale rallied to upset the Czech in three sets 2-6, 6-2, 6-3 on Sunday.
US teenager Christina McHale toppled eighth-seeded Frenchwoman Marion Bartoli in straight sets on Wednesday to reach the third round of the US Open tennis championships.
The U.S. Open's most stunning loss Wednesday was bigger than just the Grand Slam tournament, with Venus Williams withdrawing and revealing she's suffering from an autoimmune disease.
World No. 1 Caroline Wozniacki won for the first time in over a month, convincingly beating Polona Hercog in the New Haven Open, with Tuesday's play affected by an earthquake.
World number one Caroline Wozniacki's disappointing US Open preparations continued on Wednesday as she crashed out to young American Christina McHale at the ATP and WTA hardcourt tournament.