It happened in Buncrana at around 11.30am on Friday, Gardai have confirmed.
The girl was taken to Letterkenny University Hospital for treatment.
Her injuries were described by a garda spokesperson as “serious” but “non-life threatening”.
The dog was handed over to the local dog warden – a service run by Donegal County Council alongside the Irish Society for the Prevention of Cruelty to Animals.
A Garda spokesperson said that investigations into the horrific attack are ongoing.
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