They represent the governing African National Congress (ANC), the ANC Youth League, the South African Communist Party and trade union organisation Cosatu.
"Go for it, Boss!" they say to Mr Zuma, shown unbuckling his belt.
Mr Zuma is suing for damage to his reputation and damage to his dignity, the South African Press Association reports.
The demand was dated a week after the cartoon appeared but only served this week. It gives the cartoonist 14 days to pay up or face court, the agency says.
In an interview with the BBC in September, Mr Shapiro said he drew the "shocking image" of Mr Zuma as a "metaphor for what he's doing to the justice system".
He said that Mr Zuma had attempted to undermine the independence of the judiciary in order to get corruption charges "wiped off the slate".
"The aspect of Mr Zuma's own personal history of having been acquitted of a charge of rape is a secondary issue in this cartoon," he said.
"The primary issue is there's a figure about to rape the justice system with the help of his political allies," he said.
The shadow of corruption has been hanging over Mr Zuma for several years but his supporters have always maintained he is the victim of a political conspiracy.
In 2005 Mr Zuma was sacked as South Africa's deputy president when his financial adviser, Schabir Shaik, was found guilty of soliciting a bribe on behalf of Mr Zuma and jailed for 15 years in connection with an arms deal.
Mr Zuma then went on trial, but the case collapsed in 2006 when the prosecution said it was not ready to proceed.
In February 2006, Mr Zuma was acquitted of rape in a separate case, though he was widely criticised for comments about sex and HIV/Aids.
He was charged again last December shortly after winning a bitter campaign against then President Thabo Mbeki to become ANC leader.
When dismissing the corruption charges, the judge said there was evidence of political interference in the case - a statement which led President Mbeki to resign.
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