The newborn girl was swaddled in a t-shirt and wool scarf and placed in a wash basin in one of the clinic's bathrooms on Thursday, police in the German state of Hesse said.
Doctors examined the baby and determined she is about one week old and in good health. The toilet belonged to a conference centre behind the main hospital building, which has an entrance accessible to the public.
“The location where it was left leads to the assumption that the child was meant to be found quickly,” police spokesperson André Sturmeit said.
There are still no indications who the girl’s parents might be.
Media reports did not say whether the hospital had what is known as a Babyklappe or "baby hatch" in Germany, where parents can safely and legally surrender their infants to state care. Germany has some 80 baby hatches located at hospitals nationwide and 130 places where mothers can give birth anonymously.
The concept has been around for hundreds of years - the first known hatch was provided at the Vatican in the 12th Century. In Germany, mothers can place their infants in the hatch, where they find an envelope that explains their legal rights. An alarm then rings inside the hospital several minutes later, giving the mother ample time to slip away and alerting staff that there is a baby in need of care.