On Wednesday, the president sacked previous Finance Minister Nhlanhla Nene in a move that sent the rand to record lows.
His replacement for less than a week, Mr van Rooyen, was a little-known MP.
The moves come amid widespread concern over South Africa’s struggling economy.
Mr Gordhan was widely respected when he served as South Africa’s finance minister from 2009 until 2014.
His re-appointment sent the currency up, recovering from just over 16 rand to the dollar to about 15 by Monday morning, according to currency site xe.com.
But the new finance minister has a hard job with unemployment currently above 25%, growth sluggish and credit rating agency Fitch recently downgrading South Africa to one notch above “junk” status.
The brief tenure of Mr van Rooyen and the uncertainty it caused may have damaged South Africa’s reputation further, analysts say.
Mohammed Nalla, head of research at Nedbank Capital, said having a finance minister serve just a few days did not bode well.
“International investors are probably thinking: ‘Why didn’t the president make a much more considered decision in the first place?'” he said.
The leader of the opposition Democratic Alliance, Mmusi Maimane, said: “This is reckless by President Zuma – he is playing Russian roulette with the South African economy.”
A statement from Mr Zuma’s office said he had “received many representations” to reconsider his decision to appoint Mr van Rooyen.
“As a democratic government, we emphasise the importance of listening to the people and to respond to their views,” it added.
Fitch, which downgraded South Africa earlier this month, said on Thursday that Mr Nene’s sacking “raised more negative than positive questions”.
Mr Nene’s reluctance to approve a plan to build several nuclear power stations at a cost of up to $100bn is thought to have contributed to his removal as finance minister.
Mr van Rooyen will take over from Mr Gordhan as minister of co-operative governance and traditional affairs.
Marches to call for Mr Zuma’s removal as president are being planned for five cities in South Africa on Wednesday – a public holiday.
The US Federal Reserve is expected to raise interest rates on the same day in a move that could put economies in countries like South Africa under further pressure.
Former Health Minister Barbara Hogan on Friday called on Mr Zuma to resign. The highest-profile ANC member to oppose Mr Nene’s removal, she said that the president had crossed a line and needed to be held to account.
Razia Khan, an analyst with Standard Chartered bank, said the week’s turmoil was “perhaps the first instance since 2007 that Zuma has come under severe pressure within the party”.