The 43-year-old, from Plymouth, was first arrested in August over a hand-written letter sent to the Jamia Mosque in Russell Street, Eastwood, on Monday, August 1.
He was later bailed pending further inquiries.
Today the North-East Counter Terrorism Unit, which covers South Yorkshire, said the same man has been arrested again on suspicion of further offences under the Malicious Communications Act.
A spokeswoman said: "A 43 year old man from Plymouth has today been arrested on suspicion of further offences under the Malicious Communications Act.
"The man was previously arrested in August following an appeal by South Yorkshire Police in connection with reports of malicious communications. He was bailed.
"He has been taken to a local police station for questioning.
"A property in Plymouth is being searched as part of the investigation."