Ndileka Mandela, 52, has been told she should instead help revive the party.
She had earlier stated she no longer believed the ANC represented the values of her illustrious relative.
Ms Mandela said the party was neglecting to care for the poor.
"I will not be voting for something that does not resonate with me anymore, and does not resonate for what granddad and his comrades fought for," she told News 24 South Africa..
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Ms Mandela, a nurse, runs a Mandela family foundation to tackle rural poverty.
She said the ANC's recent period in power had left her feeling despondent, especially when it came to its record in wasting public money.
Ms Mandela identified the country's social care crisis and its treatment of psychiatric patients as "tipping points" that added to her loss of faith in the ANC.
But her brother was quick to urge her to re-think.
"I call on you... to reconsider your decision," News 24 reported Mandla Mandela as writing in an open letter to her.
"Please do not throw the baby out with the bathwater. What we are dissatisfied with in the ANC, it is our obligation to set right.
"The ANC has been the heartbeat of our family for many years. One can only imagine the many crises and challenges our grandfather... lived through since joining the ANC in 1944."
Mr Mandela exhorted his sister to remain within the ANC, breathe new life into it and "re-inculcate the values and principles that secured our democracy".
His letter on Friday described his sister's move as "heart-wrenching".
But Ms Mandela seems unlikely to change her mind.
"I get very incensed with people who think they knew my grandfather more than his own family did," she said on Friday.
"Nobody can actually articulate how granddad felt across the board, not just as a politician but as a father, as a family man. So you can't tell me he would be disappointed."
The ANC has held power in South Africa since Nelson Mandela was elected president in the country's first democratic elections in 1994.
The eldest granddaughter of Nelson Mandela, South Africa's first black president and an anti-apartheid icon, has been urged to reconsider her decision no longer to vote for the governing African National Congress.