There were reports that Stone, 56, and the recently single 'Mask of Zorro' star were romantically involved following his split from Melanie Griffith, reported Us magazine.
"Antonio is a brother to me, and Melanie has been with me for each and every birth of my three children. They are my family.
"I find this salacious, unkind, unfounded reporting to be the typical pretense of what passes as 'journalism' today," she said.
Banderas and Griffith parted ways earlier this month.