The actress, 50, who played Cordelia Chase in the supernatural drama series and its spin-off Angel, accused Whedon of "hostile and toxic work environments", as well as "ongoing, passive-aggressive threats" to fire her and calling her "fat" when she was four months pregnant.
Carpenter said she was prompted to speak out after actor Ray Fisher was removed from the cast of upcoming superhero film The Flash after he had publicly criticised Whedon, who had directed the reshoots of Justice League after original director Zack Snyder stepped down following a family tragedy.
A representative for Whedon said they had no comment when approached by the PA news agency.
Carpenter shared a lengthy statement on Twitter captioned "My truth. #IStandWithRayFisher."
She wrote: "For nearly two decades, I have held my tongue and even made excuses for certain events that traumatize me to this day.
"Joss Whedon abused his power on numerous occasions while working together on the sets of Buffy the Vampire Slayer and Angel.
"While he found his misconduct amusing, it only served to intensify my performance anxiety, disempower me, and alienate me from my peers.
"Last summer, when Ray Fisher publicly accused Joss of abusive and unprofessional behaviour toward the cast and crew during reshoots on the Justice League set in 2017, it gutted me.
"Joss has a history of being casually cruel. He has created hostile and toxic work environments since his early career. I know because I experienced it first-hand. Repeatedly.
"Like his ongoing, passive-aggressive threats to fire me, which wreaks havoc on a young actor's self-esteem. And callously calling me 'fat' to colleagues when I was 4 months pregnant, weighing 126 lbs.
"He was mean and biting, disparaging about others openly, and often played favourites, pitting people against one another to compete and vie for his attention and approval."
After learning she was pregnant, Carpenter claimed Whedon "proceeded to attack my character, mock my religious beliefs, accuse me of sabotaging the show, and then unceremoniously fired me the following season once I gave birth".
Carpenter said Whedon was a "vampire" who sucked the "promise and joy" out of her new motherhood.
She added: "Only recently, after years of therapy and a wake up call from the Time's Up movement, do I understand the complexities of this demoralized thinking.
"It is impossible to understand the psyche without enduring the abuse. Our society and industry vilify the victims and glorify the abusers for their accomplishments.
"The onus is on the abused with an expectation to accept and adapt to be employable. No accountability on the transgressor who sails on unscathed. Unrepentant. Remorseless.
"My hope now, by finally coming forward about these experiences, is to create space for the healing of others who I know have experienced similar serialized abuses of power."
Reporting by PA