"In light of the economic situation, I will be returning home after a highly productive week of bilateral trade and investment meetings," he said on Twitter on Sunday, scrapping plans to attend the Davos summit this week.
"We will be ably represented in Davos by Minister of Finance Mthuli Ncube", Mnangagwa said.
The protests are part of a backlash against Mnangagwa's government, which more than doubled the price of petrol and diesel last week.
In addition, Zimbabwe has been plagued by severe hard currency shortages that Mnangagwa has repeatedly promised to fix since his predecessor Robert Mugabe was deposed in a 2017 military coup.
In light of the economic situation, I will be returning home after a highly productive week of bilateral trade and investment meetings. We will be ably represented in Davos by Minister of Finance, Mthuli Ncube. The first priority is to get Zimbabwe calm, stable and working again.
The crackdown on the demonstrations has stoked fears of a return to the violent repression the of Mugabe era.
At least 12 people have been killed and dozens injured, according to the Zimbabwe Human Rights NGO Forum, which has recorded more than 240 incidents of assault and torture.
More than 600 people have been arrested, among them a prominent pastor and activist, Evan Mawarire, who has supported the protests on social media and now faces a possible 20 years in prison on a subversion charge. More than 400 people have been denied bail, said his lawyer, Beatrice Mtetwa.
On Sunday a court ruled that Mawarire has a case to answer and will hear his appeal to be released on bail on Monday.
Mawarire has called it "heartbreaking" to see the new government acting like that of former leader Mugabe, who stepped down under military pressure in late 2017 and was succeeded by former protege Mnangagwa.
There were also reports of the government imposing a total internet shutdown in response to the demonstrations.
The UN has fiercely criticised the government reaction to the protests as allegations mount of shootings, beatings and abductions of opposition figures, activists and ordinary residents.
Mnangagwa is seeking much-needed foreign investment and was in Kazakhstan on Sunday after starting his tour in Russia last Monday.
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