A letter reading, “Next time it will be a bomb you Muslim scum” was sent to the Jamia Masjid Abu Bakr mosque in Eastwood, Rotherham, on 1 August.
It was signed with a number code believed to be used by neo-Nazi groups.
A 43-year-old man from Plymouth was arrested on Friday morning under the Malicious Communications Act, the North East Counter Terrorism Unit said .
He has been detained for questioning and inquiries are continuing.
The letter sent to the mosque is believed to be one of a number sent to locations around England.
These include religious establishments, police stations and residential addresses in South Yorkshire, West Yorkshire, Bedfordshire and Avon and Somerset.