The DA says Jacob Zuma is unfit to govern after failing to repay public money used to upgrade his private residence.
The governing African National Congress (ANC) is expected to defeat the motion.
Opposition lawmakers called for speaker Baleka Mbete to step down, after accusing her of taking sides.
Baleka Mbete announced a short adjournment to consult parliamentary officials, delaying the start of the debate.
The ANC has denounced the impeachment proceedings as a publicity stunt.
The DA said it would demand a secret ballot in the hope that ANC backbenchers would defy the party by helping it obtain the two-thirds majority – 267 lawmakers out of 400 – required in the lower house, the National Assembly, to impeach Jacob Zuma.
However, Baleka Mbete has rejected the proposal, saying it is not allowed in terms of parliamentary rules, local media reports say.
The DA has 89 seats in parliament and all opposition parties combined 151.
Jacob Zuma is the first president to face an impeachment vote since minority rule ended in 1994.
He has been dogged by allegations of corruption since before he was elected president in 2009.
Jacob Zuma was accused of taking bribes over an arms deal but he denied the allegation and the charges were controversially dropped just before he took office.
He later found himself at the center of controversy over the use of $23 million of public money to upgrade his private home in the rural area of Nkandla in KwaZulu-Natal province.
In 2014, South Africa’s anti-corruption watchdog Thuli Madonsela ordered President Jacob Zuma to repay a portion of the money.
Jacob Zuma had “unduly benefited” from the building of a swimming pool, amphitheater, cattle enclosure and chicken run, Thuli Madonsela said.
The DA and left-wing Economic Freedom Fighters (EFF) party went to the Constitutional Court to challenge Jacob Zuma’s refusal to pay the money.
The court ruled against Jacob Zuma, and said the law was the “sharp and mighty sword that stands ready to chop the ugly head of impunity from its stiffened neck”.
It also condemned parliament for failing to hold Jacob Zuma accountable, and rejecting the public protector’s findings.
In a TV address to the nation on April 1, Jacob Zuma apologized for the “frustration” caused by the long-running controversy and said he would abide by the ruling.
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