Sosing reported that he had chest pains while practising before going on stage for his match.
He then informed organisers that he was experiencing numbness and muscle pain.
After on-site medical staff at Alexandra Palace made an assessment, Sosing was taken to a local hospital for further investigation.
"He has subsequently undergone neurological assessment and been diagnosed with having GBS Guillain-Barre syndrome," a statement by the PDC said.
The 41-year-old is still being cared for at the hospital at the time of writing, but he should be able to travel home soon.
"Sandro would like to thank everyone who has enquired after his wellbeing for their well wishes and kind messages," the PDC statement concluded.
White, who was scheduled to face Sosing in the first round at the World Championship, beat Ritchie Edhouse in the second round to set up a clash with Luke Littler.