Ulrich Frei said the woman had given birth to four boys and two girls – each weighing between 800 and 900 grams (about 2 pounds) – after 27 weeks of gestation on Thursday.
The woman had undergone a standard fertility treatment after unsuccessful attempts to become pregnant, Wolfgang Henrich, a doctor who assisted the delivery, told a news conference.
He said it had been an unproblematic caesarean birth.
The hospital declined to give further details about the woman.
Charite, one of Germany's leading hospitals, is 300 years old and Frei said sextuplets had never been born there before. The odds of having sextuplets is one in four billion, according to media reports.
In Germany, the survival rate of infants weighing less than 1000 grams at birth is nearly 90 percent, according to Monika Berns – director of the hospital's neonatology department.
In August, an Iraqi woman gave birth to sextuplets, but two of them died at birth due to the hospital's lack of proper medical equipment.
The first sextuplets known to have survived their infancy were born to a South African couple in January 1974.
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