Top seed Swiatek was due to begin her campaign against American Claire Liu in the second round on Thursday after being given a bye in the first round.
"You know that in and after Doha I was struggling with a strong infection," Swiatek said.
"I was allowed to play, but a strong episode of tough cough led to a rib injury. We were trying to handle it and continue to play as long as it was safe for me. We were analyzing the data in the last days and my doctor prepared my diagnosis.
"Unfortunately, I'm still feeling a lot of discomfort and pain and I can't compete."
Swiatek added that the injury would also keep her out of Poland's Billie Jean King Cup qualifier against Kazakhstan in mid-April.
"I will keep you updated about where I play next, because it depends on my process of recovering and the recommendation of my medical team," she added.
