Officers from Counter Terrorism Policing North East have arrested the 31-year-old on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under section 41 of the Terrorism Act 2000.
Three other men, aged 22, 36 and 41, were arrested at addresses in Sheffield on suspicion of the same offence.
The men have been taken to a police station in West Yorkshire for questioning.
The arrests were intelligence led and pre planned as part of an ongoing investigation by Counter Terrorism Policing North East.
Three properties in Sheffield and one in Chesterfield are currently being searched in connection with these arrests.
Police said they were aware local people may have concerns as a result of the police activity in the area and are asking people to remain alert but not alarmed. They added that they were grateful for the assistance and understanding of people locally.
Residents will be kept as informed as possible and officers are grateful for their understanding, patience and support while these enquiries continue.