Boutier will become the first golfer from France, man or woman, to be ranked number one if she finishes solo third or better on Sunday at the Jian Lake Blue Bay course on Hainan Island.
"Lilia Vu has withdrawn from the Blue Bay LPGA before the second round due to injury," the LPGA Tour said, without elaborating.
World number three Boutier has ground to make up to finish in the top three.
She was nine shots off the lead going into the weekend after a second-round one-under 71 left her at level par for the tournament.
The lead is shared by South Korea's An Na-rin on nine-under 135, after a second-round 65, and American Sarah Schmelzel, who continued her recent good form with a 69 to follow her opening 66.
Australia's Minjee Lee led overnight, but is two shots back after a level-par 72 on Friday in the $2.2 million (£1.7m) event that concludes a three-tournament Asian swing.
Boutier, 30, who won her first major last season at the Evian Championship in her native France, was second last week at the HSBC Women's World Championship in Singapore, a shot behind winner Hannah Green of Australia.
The Frenchwoman will need a big improvement on Saturday and Sunday to get into the third place she needs, which is currently held by South Korea's Choi Hye-jin on eight under par.
Boutier, now in her eighth season on the LPGA Tour, finished third in her only previous appearance at Blue Bay in 2018.
The 26-year-old American Vu has been struggling with back issues and also withdrew during the final round in Singapore five days ago.
"Yeah, last week my body wasn't feeling great overall physically, and it was just Sunday that I couldn't handle," she admitted on Tuesday.
Vu had carded a level-par 72 in the opening round of the Blue Bay on Thursday before pulling out.
