The 47-year-old TV personality backed allegations of ageism which have been directed at the BBC in recent days.
BBC One controller Jay Hunt announced that Phillips, 66, had been axed in favour of 30-year-old Dixon last week - as first rumoured in June.
Writing in her column for the Daily Express, Feltz commented: "Somewhere it is written that when a woman reaches a certain age she must be bundled out of sight and stuck far away where no one is in danger of traumatising themselves by looking at her haggard visage.
"It happened years ago to accomplished travel presenter Anne Greg. It happened to Anna Ford and Moira Stewart. Now Strictly's Arlene Phillips has been judged 'past her view-by date' and put out to pasture."
She added: "At 66, Arlene is experienced, knowledgeable, a seasoned professional and a valuable part of Strictly Come Dancing. Her successor Alesha Dixon is easy on the eye and an effervescent dancer but can't come close to Arlene's expertise. Alesha should have been an 'also', not an 'instead of'."
Former Strictly stars Fiona Phillips, Rachel Stevens and Louisa Lytton have all backed Arlene since the revamp was confirmed.