The former world No 1 and 23-time Grand Slam champion gave birth to daughter Alexis Olympia Ohanian Jr last September.
The American only made her competitive return earlier this month and it is not known which majors she will take part in this season.
But Williams admitted she was left scared following the delivery.
In an article for CNN, she wrote: “I am lucky to have survived.
“My daughter was born by emergency C-section after her heart rate dropped dramatically during contractions. The surgery went smoothly.
“But what followed just 24 hours after giving birth were six days of uncertainty.”
Discussing in detail about the complications surrounding the delivery, she added: “It began with a pulmonary embolism, which is a condition in which one or more arteries in the lungs becomes blocked by a blood clot.
“Because of my medical history with this problem, I live in fear of this situation.
“So, when I fell short of breath, I didn’t wait a second to alert the nurses.
“First my C-section wound popped open due to the intense coughing I endured as a result of the embolism.
“I returned to surgery, where the doctors found a large haematoma, a swelling of clotted blood, in my abdomen.
“When I finally made it home to my family, I had to spend the first six weeks of motherhood in bed.”