West Midlands police said the 36-year-old was arrested at an address in Warwickshire on Saturday evening.
According to a report in The Sun, the This Morning presenter, 48, has paid out large sums after falling victim.
It is alleged the Birmingham-born celebrity had been threatened that lies would be spread about her if she did not co-operate with demands.
Police said the man remains in custody for questioning.
Earlier, West Midlands Police said inquiries into the alleged blackmailing were progressing swiftly.
"We are investigating an allegation of blackmail of a woman in her 40s," the force said in a statement.
"We take reports of this kind very seriously."
The presenter came to prominence as a contestant on the third series of Big Brother in 2002.
She was promoted to co-presenter of This Morning in 2020, appearing alongside Dermot O'Leary on Fridays.
There have also been appearances on I'm a Celebrity... Get Me Out of Here! in 2010 and Strictly Come Dancing in 2014.
Last week she was announced as the new co-host of The Great British Bake Off, replacing Matt Lucas.
She also appeared alongside actor Richard E Grant to host the 2023 Baftas.