The incident took place in Bad Koenig, some 30 miles southeast of Frankfurt in Hesse state. Police said they were yet to establish why the dog attacked the child
The dog has been taken to an animal shelter in nearby Michelstadt, according to Bild.
The breed of the dog remains unclear. A police spokeswoman described the animal as a Staffordshire mix while shelter staff referred to a boxer mix, acting “very aggressively”.
A local news website, hessenschau.de, said the baby was bitten on Monday and taken to hospital, where its condition was stabilised, but that it later died on Monday night.
The incident took place almost a week after two people were killed by a dog in northern Germany.
A 52-year-old woman and her 27-year-old son were killed by a Staffordshire terrier they owned on April 3 in Hannover.