Cleveland Police said they were called to Dale Street in the village near Redcar on Tuesday morning.
The girl is is a critical condition at the Royal Victoria Infirmary in Newcastle.
The force said a 26-year-old man was arrested but refused to say what it was on suspicion of.
A spokeswoman said: “Officers are continuing with their inquiries into the circumstances around how the child came about her injuries.
“A 26-year-old man was arrested in connection with the incident and he remains in police custody.”
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