A candidate at Voroni Primary School in Kwale County gave birth to a boy after the national examinations began on Tuesday.
Kwale County Commissioner Karuku Ngumo said the girl started having labour pains earlier in the day so she was taken to Kwale Hospital.
A source at the hospital said she was stable and that she wrote the mathematics test from her hospital bed.
"We are happy that the girl delivered without any complications," the source said.
This was the first such case to be reported in the county this year.
The examinations kicked off smoothly, with a total of 8,086 candidates across Kwale.
Mr Karuku said security was beefed up in all examination centres so they were not anticipating any problems.
“We have tightened security in all our institutions to ensure the examinations run smoothly on the three days," he said.
Education officials, including Cabinet Secretary Amina Mohamed, Principal Secretary Belio Kipsang, Teachers Service Commission chief executive Nancy Macharia and Kenya National Examination Council board chairman George Magoha were at various stations as early as 6am to supervise the opening of exam containers.
Security has been tightened across the country to prevent interruptions.
In Kajiado County, a watchman was arrested for trying to sneak fake papers into an examination centre on Monday night.
In Kakamega County, a man was apprehended for allegedly posing as a candidate during music practicals at Mukuyu Girls' Secondary School.
Meanwhile, the CS said all the candidates, numbering more than a million, will get chances to join secondary schools.