The currency is down by 1.7% at 12.9929 per dollar as of 8:08 a.m. ET after being down by about 2.9% earlier.
Zuma reportedly told senior leaders of the South African Communist Party that he plans to fire Pravin Gordhan, the country's respected finance minister, Bloomberg's Sam Mkokeli reported earlier on Tuesday, citing "three people with knowledge of the matter."
On Monday, Zuma instructed Gordhan to return immediately from an investor roadshow to Britain and the US "without giving a reason for the decision." The rand fell by about 3% in the aftermath.
"These falls underline the importance that markets place on Mr. Gordhan," John Ashbourne, Africa economist at Capital Economics, wrote. "Were Pravin Gordhan to actually be removed, we think that the rand could fall by another 5% against the dollar. [...] Even if Mr. Gordhan himself is not removed from office, a reshuffle could still have a significant market impact."
The South African currency has fallen after unexpected political appointments and rumors on several occasions over the last few years.
Back in December 2015, Zuma fired his respected finance minister Nhlanhla Nene and replaced him with a virtually unknown former mayor, David van Rooyen. Just days later, Zuma fired the latter and replaced him with Gordhan. Then, in mid-2016, the rand tumbled amid rumors that Gordhan might be fired.
"In any event, tensions within the ruling African National Congress will escalate this year," added Ashbourne. "President Zuma is set to resign as the head of the party in late 2017 and as state president in 2019. The struggle to succeed him - which will probably include several painful market surprises - is only now beginning in earnest."