"We are actively taking this matter up by opening a charge of defamation and malicious conduct," African National Congress (ANC) spokesperson Jackson Mthembu said in a statement.
"We will also be approaching relevant recourse structures that deal with elections including the Independent Electoral Commission and the electoral court if necessary to ensure that this irresponsible conduct is curtailed and exposed."
Mthembu said the SMS was based on a "deliberate lie" and targeted Zuma.
The text message, which was sent to prospective voters, read: "The Nkandla report shows how [President Jacob] Zuma stole your money to build his R246m home. Vote DA on 7 May to beat corruption. Together for change."
Democratic Alliance (DA) parliamentary leader Lindiwe Mazibuko hit back and welcomed the court challenge.
"The DA welcomes the opportunity to go to court to defend our efforts to ensure accountability for the Nkandlagate scandal," she said.
"We will tell the judge exactly what the rest of South Africa was told this past week, that president Zuma improperly and materially benefited from the R246-million so-called security upgrade of his private home in Nkandla."
She said the ANC was blindly protecting Zuma.
"Instead of doing everything possible to ensure that President Zuma is removed from office and made to apologise for this wrongdoing, they would rather spend their time and energy trying to hide the truth from the country.
"This will not work. South Africans are rightly outraged by this serious maladministration which has diverted much-needed public money from the poor in order to benefit one man. This is a shame that warrants the president being fired from his post, not blindly protected."
She suggested that the ANC re-examine Public Protector Thuli Madonsela's report as it was clear they missed some key details.
"The rot in Jacob Zuma's ANC has now reached crisis proportions," she said.
"The leadership of the party can no longer see the difference between right and wrong. They see only through the prism of keeping power in the hands of President Zuma. "
Public protector's report
Madonsela this week found that Zuma and his family had improperly benefited from R215-million security upgrades to his Nkandla home. This was paid for by government. Outstanding work on the property was around R36-million.
"It is common cause that in the name of security, government built for the president and his family in his private [home], a visitors' centre, cattle kraal and chicken run, swimming pool, and amphitheatre among others," she said in her findings.
The Economic Freedom Fighters and the DA have since opened criminal cases of corruption against Zuma. – Sapa