A senior member of the South African Communist Party, which is in an alliance with the ANC, said that Zuma told its leaders that he planned to fire Gordhan and his deputy Mcebisi Jonas.
"While there are many outstanding cabinet ministers with integrity and who are performing exceptionally well in their portfolios, however, we need to admit that there are also several serving ministers whose performance is rather unsatisfactory, hence they have attracted severe criticism as public representatives against whom appropriate action would be expected".
Investors were already fretting about Gordhan's job security after Zuma on Monday ordered him to cancel a series of meetings with foreign investors and return home. Later on Friday morning the rand was trading below R13.50 against the greenback while the bond market has seen the 10-year bond yield peak at 9% Thursday - up from 8.3% a week ago.
Gigaba, though, said he was committed to protecting South Africa's cherished investment-grade credit ratings, which analysts have said are threatened after Gordhan's removal. Confronted with persistent allegations of corruption and nepotism, Zuma has faced mounting pressure from within the party to resign.
Opposition parties have again called for a motion of no confidence as his choice of ministers comes under the spotlight.
"Zuma has bowed to the whims of those who determined to enrich themselves at the expense of the poor and jobless", the country's main opposition party, the Democratic Alliance, tweeted after the announcement.
Mcebsi Jonas, ANC party leader in Parliament, commented that the ousted cabinet members' "crime is incorruptibility".
But South Africa remains one of the world's most unequal societies, riven by glaring income disparities, an official jobless rate of 26.5 percent, and widespread poverty. The outcry by funeral-goers including the ex-wife of Nelson Mandela, Winnie Madikizela Mandela, further exposed the ruling party's divide.
In a statement, Zuma said he had chose to make changes to the National Executive in order to improve efficiency and effectiveness.
Gordhan's replacement Gigaba is a Zuma-ally who was criticized for extreme tightening of immigration rules while minister of home affairs.
South Africa's new finance minister has pledged to "radically transform" his country's economy, signalling a dramatic swing to the left less than 48 hours after taking up his post.
He added that the president has the right to reshuffle his Cabinet and exercise his own choices. Much of the ANC leadership is appalled by this, as well they should be. The ministers and deputy ministers new to cabinet taking the oath of office.
Malusi Gigaba was appointed after president Jacob Zuma sacked his widely respected predecessor, Pravin Gordhan, in an overnight cabinet purge last week.
Last October, Mr Gordhan was charged with fraud but the charges were later dropped. Even his deputy president, Cyril Ramaphosa, called the move "totally, totally unacceptable". His term extends into 2019 but the ANC is likely to choose his successor in December.