Black people could no longer be treated as “sub-humans”, it said.
The nation has been gripped by a racism row after Penny Sparrow, an opposition Democratic Alliance (DA) member, on Facebook called black people “monkeys”.
She denied she was a racist. The DA party suspended her membership.
The racially discriminatory apartheid system ended in South Africa in 1994. It had been introduced in 1948 by the then-white minority government and was later declared by the UN as a crime against humanity.
A spokesman for the ANC chief whip’s office, Moloto Mothapo, told the BBC that current legislation was insufficient to tackle racism.
“We haven’t had a single person imprisoned for racism despite many instances of racism. We don’t believe it addresses the crime of racism,” he said.
A statement issued by the ANC parliamentary chief whip’s office said racial bigotry and apartheid should be considered a serious human rights violations punishable by imprisonment because of South Africa’s “painful past”.
“Elsewhere glorification of Nazism and denial of Holocaust is a crime and perpetrators are tried and sentenced to a prison term,” it added.
The ANC also said it had filed criminal charges against several DA members – including Ms Sparrow and MP Dianne Kohler Barnard.
Ms Kohler Barnard was expelled from the DA in October after she shared a post on Facebook which suggested that public services in South Africa were better during apartheid and called for the return of former President PW Botha.
She won an appeal against her expulsion from the party, and was instead ordered to pay 20,000 rand ($1,320; £888) to a charity working with communities disadvantaged by apartheid.
On Monday, the DA said it had filed charges against Ms Sparrow “for infringing the dignity of all South Africans and for dehumanising black South Africans” as it did not tolerate racism.
On Facebook, Ms Sparrow used the word monkeys to describe New Year’s revellers on the beach in the eastern city of Durban because of the mess she said they made.
She later apologised but was condemned by many on social media and the hashtag #RacismMustFall was trending on Twitter.
The South African Human Rights Commission, a statutory body, is also investigating her comments.