A letter issued by the Regulatory Authority of the Post and Telecommunications of Congo (ARPTC) states that Facebook, Twitter, Skype, YouTube and LinkedIn should be blocked temporarily from 1800 GMT on Sunday.
Kabila's last term comes to an end on Sunday but the country's Constitutional Court has ruled that he can stay on until a successor is elected.
Elections have been postponed till April 2018 after the electoral commission complained of inadequate resources to conduct the process.
The opposition has accused Kabila of manipulating the system to cling on to power and is calling for protests to start on Monday.
"It's not surprising that Kabila's government is cracking down on social media," Phil Clark, a political scientist specialising in conflict and post-conflict issues in Africa at London's Soas, told RFI. "Kabila is mostly worried about a very young and mainly urban protest movement that's been out on the street for the last few months."
Kabila's refusal to step down will infuriate his opponents, Clark predicts. "And Kabila is trying to take away from them some of their major tools of mobilisation, particularly social media - Facebook, Twitter, Skype, WhatsApp. These tools are central to this protest movement, and Kabila is trying to block that as quickly as he can."
Human rights groups have called for the government to lift the directive.
"This announcement of a blackout of social media is a blatant attempt to keep the Congolese people in the dark at a critical time," says Evie Francq, DRC researcher for Amnesty International. "This is a restriction of freedom to express themselves and access information. 19 December is an important date and people have the right to know what's going on."
This is not the first time the DRC government has resorted to imposing media blackouts.
In January 2015 the government shut down the internet and blocked SMS services for mobile phones throughout the country following deadly clashes with the police.
"It's a reaction of urgency, emergency," Julie Owono of the Internet Without Borders NGO says. "Usually, regimes which resort to internet censorship or blackout are mostly and more importantly preoccupied by the image they will have and also by the free flow of information, which will obviously tarnish their image."
The DRC is under the international spotlight, she points out. "So if you let images and photos flow freely, showing how your police is targeting civilians and unarmed protesters, even when accused of killing these people, obviously this is not very good for your image."
But the authorities have failed to understand how the cyberworld works, she argues. "We've seen that on the internet, whenever you're trying to hide or censor something, the more it will become visible because nobody likes hidden things. So if you're hiding something, it means that that thing happens to be very important. So it's very counterproductive."
Why won't Kabila go?
There seem to be several reasons why Kabila is clinging so hard to power.
One of them may be because of his financial interests.
Financial news service Bloomberg has just released a report on the Kabila family's involvement in the country's economy.
"The Kabila family empire really extends into every single corner of the Congolese economy," Thomas Wilson, one of the journalists who worked on the report, told RFI. "So they have assets in mining, in telecoms, in banking, in transport, in food distribution and many more. In addition to that, we were able to trace companies registered in foreign countries as well."
He says they have uncovered a web of dubious activities, such as a payment made by the UN for a police station, that ended up in the hands of the Kabila family and claims some deals could have hurt the DRC's economy.
"We believe that the participation of some members of the presidential family in certain transactions in the Congolese economy, specifically the suspension of the IMF loan programme in 2012, which we've identified is the result of the Congolese government refusing to publish contracts related to the sale of a mining asset. And in that particular transaction we identified a member of the presidential family to have been a shareholder in that mining project."
The team also believe they have evidence that the Kabila family's interests have frightened off other investors.
"So there is evidence that suggest that the politicisation of certain aspects of the Congolese economy has, at times, prevented development rather than encouraged it."
Kabila could also be worried about his own personal security.
"What happens if he steps down and loses control of the police and the armed forces, does that leave him open to attack?" asks Phil Clark.
"But I think he's also worried about international justice. He has seen his major political opponent Jean-Pierre Bemba convicted and sentenced by the International Criminal Court. Kabila has been able to protect himself against prosecution by using his power, but if he steps down and he looses that kind of diplomatic power, then he could find himself facing a similar fate."
Violence to be expected
"We're going to see instability and we're going to see protests and those protests we're seeing now are going to face a very violent crackdown. There's not even going to be a pretence of trying to allow for peaceful protest," says Alex Fielding, an intelligence and security analyst with Max Security Solutions.
"Already now they've banned political protest in most parts of the country, including Kinshasa, so the government will basically use that ban to say that any gathering will be met with force, and that's going to cause violence. That's going to cost lives and that's going to cause broader instability in the political realm, as well."
The main opposition coalition led by Étienne Tshisekedi has already organised a series of protests that have been met with violence by the police.
Their planned protests on 19 December are likely to face a further crackdown.