Badly injured people streamed into a hospital in the capital Harare after alleged assaults by security forces.
"Our country is going through one of the most trying periods in its history," the Zimbabwe Catholic Bishops' Conference said in a statement lamenting the government's "intolerant handling of dissent" and its failure to halt economic collapse.
Media group MISA-Zimbabwe shared a text message from the country's largest telecom company, Econet, calling the government's internet order "beyond our reasonable control".
The High Court will hear a challenge to the shutdown on Monday, the Zimbabwe Lawyers for Human Rights said.
A prominent pastor and activist who faces a possible 20 years in prison on a subversion charge arrived at court, one of more than 600 people arrested this week.
Evan Mawarire (pictured below) has called it "heartbreaking" to see the new government of President Emmerson Mnangagwa acting like that of former leader Robert Mugabe.
Mawarire is accused of inciting civil disobedience online. "It's a shame what's happening," the pastor said.
International calls for restraint by Zimbabwe's security forces are growing, while Mr Mnangagwa prepares to plead for more investment at the World Economic Forum in Davos, Switzerland.
He announced the fuel price increase on the eve of his overseas trip, leaving hardline former military commander and Vice President Constantino Chiwenga as acting president.
Petrol in the economically shattered country is now among the most expensive in the world. Zimbabweans heeded a nationwide stay-at-home call earlier this week in protest.
Rights groups and others have accused security forces of targeting activists and labour leaders in response, with the United States expressing alarm.
The UN human rights office on Friday urged Zimbabwe to stop the crackdown, noting reports of intimidating door-to-door searches by security forces.
The Zimbabwe Association of Doctors for Human Rights has said it had treated 68 cases of gunshot wounds and 100-plus other cases of "assaults with sharp objects, booted feet, baton sticks" and more.
Injured people streamed into a private hospital in the capital, Harare, on Thursday. Some had broken legs. A nurse attended to a man with a broken spine.
Albert Taurai said he had ventured out to look for bread when plainclothes officers wearing masks beat him up, accusing him of barricading roads.
Keith Frymore, a 21-year-old security guard, had a torn lip. He told the AP a group of uniformed soldiers attacked him at work.
Other hungry Harare residents who ventured out seeking food have reported being tear-gassed by police. Soldiers were still controlling long fuel queues in the capital on Friday, and many wary residents stayed at home.
Zimbabweans had briefly rejoiced when Mr Mnangagwa succeeded Mr Mugabe, who was forced out in late 2017, thinking the new president would deliver on his refrain that the country "is open for business".
But frustration has risen over the lack of improvement in the collapsed economy, which doesn't even have a currency of its own.
The internet shutdown cuts off crucial access to the mobile money that Zimbabwe's government uses to pay teachers and other public workers. Some said they can no longer afford fares for public transport, and some shops have run out of basics such as bread.
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