A 29-year-old man was arrested at an address in the city by officers from West Midlands Police's counter-terrorism unit, the force said.
A 28-year-old woman taken into custody earlier has been bailed.
Officers are continuing to search three addresses in the Foleshill and Radford areas. Police say the arrests were intelligence-led.
The latest arrest was pre-planned and there is no risk to public safety, said the force.
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