The 28-year-old is believed to have started to have contractions when she got to the car park at the airport and rushed back inside to give birth in the toilet.
After delivering the infant, she is accused of putting her hand over its nose and mouth until it stopped breathing.
It is alleged Beate and her 25-year-old boyfriend then wrapped the tiny body in a jacket and stowed it in a travel bag.
The young father then drove with the baby to their flat in the city of Siegen.
As Beate was bleeding heavily, she stayed at the airport and called for help, according to reports.
Emergency services were called and the woman told paramedics that she had miscarried four weeks ago and still had some bleeding.
Chief Prosecutor Ulrich Bremer said: "[To the doctor] it was clear that the woman must have given birth only shortly before."
Beate G. admitted she delivered a child at the airport when doctors alerted the police, who then paid a visit to the couple's home and found the dead infant in the bag.
Beate G. faces one count of manslaughter and her partner one of manslaughter by omission
The case was the second airport baby dumping case reported in Europe in the last week.
Police arrested a mother for throwing her newborn baby into a bin in an airport toilet because she did not want to miss her connecting flight to America.
The baby was discovered in a plastic bag in the toilet’s bin by a cleaner at Vienna's Schwechat International Airport in Austria.
Employees from the cleaning service found the baby at 1.30am and then shortly before 2am the authorities found the 27-year-old Nigerian mother sleeping in the waiting area covered in blood.
Authorities confirmed that the woman, who is a student, was the baby's mother.
It was reported that the woman was flying from Minsk, the capital of Belarus, to Washington D.C.
She claimed she threw the infant away in order to not miss her connecting flight.
She also claimed she thought the baby was stillborn, although reports said the infant died in hospital.