The veteran TV star, who is best known for presenting ITV's Wish You Were Here? for more than 30 years, admitted that she felt furious when the news was announced earlier this month.
Phillips, 66, will be replaced by former Strictly champ Alesha Dixon, 30, when the hit BBC One ballroom show returns in the autumn.
Speaking to The Mirror, Chalmers claimed: "It's obvious they have just gone for looks. It's a great shame because Arlene really knew her stuff. Are you going to tell me Alesha Dixon will have that authority? It's age discrimination and is disgraceful, really."
The 72-year-old presenter also commented on rumours that the programme's professional competitors are annoyed over Dixon's appointment.
She said: "I understand the resentment of professional dancers having to take criticism from someone who is so inexperienced and has not been a judge."
TV personality Vanessa Feltz, former Blue Peter host Valerie Singleton and Labour's deputy leader Harriet Harman have also criticised the Strictly revamp in recent days.