Not even the tennis dynamo Serena Williams is immune from the complications and challenges new mothers face during and after childbirth.

In a Vogue cover story published online on Wednesday, Ms. Williams, who holds 23 Grand Slam titles — some call her a superhero, others a queen — shared her agonizing postnatal experience, including an episode in which hospital employees did not act on her concern that she was experiencing a pulmonary embolism, a sudden blockage of an artery in the lung by a blood clot. She is prone to such clots, a condition that nearly killed her in 2011.

“Serena lives in fear of blood clots,” the Vogue article said.

On Sept. 2, the day after giving birth to her daughter via cesarean section, Ms. Williams was having trouble breathing and “immediately assumed she was having another pulmonary embolism,” the article says.

She alerted a nurse to what she felt was happening in her body and asked for a CT scan and a blood thinner, but the nurse suggested that pain medication had perhaps left Ms. Williams confused, according to Vogue. Ms. Williams insisted, but a doctor instead performed an ultrasound of her legs.