Mr Motlanthe is a senior ANC member whose comments show growing disillusionment with the party.
The party has won each general election with more than 60% of the vote since white minority rule ended in 1994.
However, it lost some of South Africa's main cities - including the commercial capital, Johannesburg - in local elections in 2014.
Voters were seen to have punished the party because of worsening corruption within its ranks.
Its leader, President Jacob Zuma, has survived eight no-confidence votes in parliament.
He has been accused by the opposition and his ANC critics of being at the centre of a corrupt network in government, an allegation he denies.
In the interview with BBC HARDtalk, Mr Motlanthe said the electorate will vote out the ANC for as long as it is "associated with corruption and failure".
"It would be good for the ANC itself and let me tell you why - because those elements who are in it for the largesse will quit it, will desert it and only then would the possibility arise for salvaging whatever is left of it," Mr Motlanthe added.
Mr Motlanthe served as South Africa's president between 2008 and 2009.
He was closely allied with Mr Zuma, but later fell out with him.
Mr Zuma is due to step down as ANC leader in December and as president in 2019.
He is backing his ex-wife and former African Union commission chairman woman, Nkosazana Dlamini-Zuma, to succeed him.
Her main challenger is Mr Zuma's deputy and former business tycoon Cyril Ramaphosa.
- 2005: Charged with corruption over a multi-billion dollar 1999 arms deal - charges dropped shortly before he becomes president in 2009.
- 2005: Charged with raping a family friend - acquitted in 2006
- 2016: a court ordered he should be charged with 786 counts of corruption over the arms deal - he has appealed
- 2016: Court rules he breached his oath of office by using government money to upgrade private home in Nkandla - he has repaid the money
- 2017: Public protector calls for a judge-led inquiry into allegations he profiteered from relationship with wealthy Gupta family - he denies allegations, as have the Guptas
- No inquiry appointed yet