Hoeneß, 62, who is soon due to start a three-and-a-half year prison term, contacted police over the weekend after the letter demanding €200,000 arrived at his home in Bad Wiessee in Bavaria.
Bild newspaper reported that the letter said the former Bayern president could be attacked in prison - and his family hurt while he was away - if he failed to pay up.
The police and Hoeneß set up a sting, arranging to meet the man who had sent the letter - and promising to hand over the money.
But the 50-year-old man who turned up at the rendezvous in Munich was arrested.
A police statement confirmed the blackmail attempt. "In the extortion letter Mr Hoeneß was threatened with serious difficulties during his upcoming criminal detention. Mr Hoeneß could get these difficulties to go away by paying a six-figure cash sum.”
They said the man had been held in custody since Saturday evening.
The former Bayern Munich president and player was sentenced in March to three years and six months in prison for evading more than €28 million in taxes.