Netanyahu and Peres have no plan to attend the event in Johannesburg's Soccer City stadium on Tuesday, officials said on Monday, citing costs and health reasons.
Peres, 90, had been advised by his doctors not to make the trip, according to aides.
"The president is recovering from flu and doctors advised him not to fly," a spokesman for Peres claimed.
Israel was an ally of South Africa's former apartheid rulers whose racial segregation Mandela fought and resisted, getting jailed for 27 years on Robben Island after being convicted of treason for his campaign.
Palestinians, who hail South Africa's first black leader as an inspiration in a conflict with Israeli apartheid, will be represented by acting Palestinian Authority Chief Mahmoud Abbas - one of about 70 world leaders South Africa expects to pay their respects.
Netanyahu hailed Mandela as "a freedom fighter who rejected violence", although the African National Congress's struggle against apartheid initially proved violent, leading Mandela to being labeled a "terrorist" by the US, Israel's major ally.
Mandela was only removed from the US terror list in 2008.
A foreign ministry official said the speaker of parliament or a cabinet minister could represent Israel at the funeral.
In 2010, Peres denied a newspaper report that Israel had offered to provide the apartheid state with nuclear weapons in 1975.
NTJ/BA