Initial reports from the Public Safety Bureau in Xinjiang province said an "elementary inspection" of the body of 23-year-old Ma Ailun, a former flight attendant, showed "an obvious electronic injury" on her neck.
Local police said they had not yet determined if Ma's phone was involved in her July 11 death.
“We are deeply saddened to learn of this tragic incident and offer our condolences to the Ma family," Apple said in a statement. "We will fully investigate and cooperate with authorities in this matter.”
A woman who said she was Ma's sister, posting to the Chinese social network Sina Weibo, alleged the iPhone was responsible for her death.
"I hope that Apple Inc. can give us an explanation," she wrote. "i also hope that all you will refrain from using your mobile devices while charging."
Local reports drew heavily on the Weibo feed of the supposed sister, whose identity could not be verified, and thus vary on the specific details of the case.
The phone was supposedly purchased in December, but it was not clear if it was the most recent iPhone 5 or a previous model.
Speculation focused particularly on the type of charger Ma used, as a "flood" of uncertified power chargers has recently hit the market,
A warning from the China Consumers' Association in May said the chargers could turn the smartphones into "pocket grenades" that could cause explosions, electric shock or fires.
Her family said she was in the bath when she received the call, but got out to answer, and claimed she was using genuine Apple parts.