The man, 20, is being investigated after little McKenzie Ellis died following a brave three-day battle against at London's Kings College Hospital on July 26.
The tot was left in a critical condition after suffering a severe head wound at home in Broadstairs, Kent.
The dad told nurses that McKenzie fell from his arms during a feed.
An inquest into his death was postponed pending the outcome of the investigation.
A spokesman for Kent Police said: " Kent Police is investigating after the death of a baby from Broadstairs.
Officers were called on Monday 23 July after the infant was taken to hospital in a critical condition.
The baby was transferred to a London hospital and later died on 26 July.
A 20-year-old man from Broadstairs was arrested in connection with the incident and has been released on bail until 15 August whilst enquiries continue."
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