The 'Papi' singer and her then-husband Marc Anthony rushed Emme to hospital three years ago to undergo a number of medical tests, including an MRI scan.
"I just remember that feeling of, 'Something is wrong with that baby and I'm gonna die'," she told CNN's upcoming Big Stars, Big Giving special. "I remember looking at Marc and going, 'We should call the doctor'.
"I started panicking a little bit and he was panicking, too, because…we were thinking, 'Did somebody drop her when we weren't looking?'"
"I just remember looking at him and saying, 'If Emme's not going to be okay, I'm not going to be okay'. He's like, 'I'm not going to be okay - none of us are going to be okay'."
Emme was, however, given the all-clear.
Lopez previously said that the incident, which took place shortly after the birth of Emme and her twin brother Max in February 2008, made her feel grateful that she was able to afford medical treatment.
"I started to wonder - what if I couldn't afford a doctor, or receive the medicines, the procedures?" she revealed a year after the twins were born.
The health scare also prompted Lopez and her sister to launch the Maribel Foundation, which is dedicated to improving the health and well-being of women and children. The organisation is named for Anthony's sister, who died of brain cancer aged 9.
Lopez and Anthony announced their divorce back in July.