Security experts warn that African governments and commercial online services are vulnerable to criminals, who have the potential to disrupt critical infrastructure.
But critics say that these laws could also be used to clamp down on the use of online platforms that promote good governance, express dissent and mobilize citizen engagement.
The measures have not only been implemented in countries known for strict media controls such as Ethiopia, but are also being introduced in democracies such as Kenya and South Africa.
While rising internet use is driving the rapid growth of the digital economy and enhancing access to information and government services in Africa, it has also exposed users to new and sophisticated threats.
The two largest economies in Africa - South Africa and Nigeria - are each estimated to lose $500m (Â£375m) annually to cyber criminals, according to a 2016 McAfee report.
In addition, African governments are fighting against local and international hacktivist groups who have carried out several disruptive attacks in recent years.
Anonymous Africa claimed responsibility for several attacks that targeted the website of the South African Broadcasting Corporation (SABC) in July over the broadcaster's ban on broadcasting violent protests.
The group also shut down the website of the Zimbabwe's ruling Zanu-PF in support of anti-government protests.
Many African governments have appeared unprepared for these threats and are now racing to tighten their telecom laws.
With social media platforms being used to organise political activity, the continent's political elite seems worried that such platforms could be used to foment revolt.
In the past months, authorities in Uganda, Gabon, Chad, Burundi and Congo-Brazzaville have shut down internet services during disputed elections, raising fears that more governments could take similar measures.
Over the past year, South Africa, Ethiopia, Kenya, Nigeria, Angola, Madagascar and Zimbabwe have passed or proposed stringent laws to fight real and imagined threats.
South Africa has been accused of proposing "Africa's worst new internet censorship law".
The draft Films and Publications Amendment Bill seeks to "protect the public and children", but critics say its vague language and definitions  will "stifle the empowering, democratising potential of the internet" and scare away potential business investors.
In June, Ethiopia passed the Computer Crime Proclamation, which criminalises defamatory speech, spam and pornography, among other offences, with jail sentences of up to 10 years.
Activists say it could also be used to silence government critics, who are reliant on online publishing due to the country's rigid media controls.
In Nigeria, journalists and bloggers have criticised the 2015 Cyber Crime (Prohibition, Prevention, Etc) Act, saying it has been used by politicians to curtail freedom of expression. Two prominent bloggers have been arrested on allegations of "cyber stalking" under the Act.
Kenya is preparing legislation to curb cyber crime and regulate social media, and has been accused of plotting to use the law to shut down social media. The government already has a history of going after internet users: Among Kenyan social media users arrested in 2015 was a prominent blogger accused of insulting the president.
Kenyan officials have also blamed "the spread of hate speech" on unregulated social media use. The law is expected to be implemented before the August 2017 general elections.
The Zimbabwe government, long intolerant of dissent, is planning to pass a law which has been criticised for banning the use of anti-censorship software. The proposed law also outlaws social media groups based on racial or tribal identity.
Information Minister Supa Mandiwanzira said there was a need to pass laws that protect internet users against defamation and hacking, but the Matabeleland Institute for Human Rights urged parliament and citizens to defend human rights "as it grossly violates human rights".
While these laws provide a legal framework to fight cyber crime and control the dissemination of hate speech, they could also provide a basis for authoritarian regimes to intimidate their rivals.
In June, Isaac Habakuk Emily from northern Tanzania was jailed for three years after he was found guilty of insulting President John Magufuli in a Facebook post contrary to the country's CyberCrime Act of 2015. He is said to have referred to the president as an "imbecile".
Tanzanian law allows for a minimum fine of 3m shillings ($1,375; Â£1,000) and minimum jail term of three months for publishing false, deceptive or misleading information on a computer system.
In Zimbabwe, spokesperson for the People First party, Jealousy Mawarire, was last month charged over a tweet accusing Education Minister Jonathan Moyo of financial impropriety.
With the cybercrime bill still in the draft stage, he was charged under the old Posts and Telecommunications Act, which outlaws the sending "by telephone any message that is grossly offensive or is of an indecent, obscene or threatening character".
In Nigeria, the Bauchi State authorities arrested Musa Azare, a journalist and blogger in June on allegations of "cyber stalking" the governor. This came shortly after another blogger, Abubakar Sadiq, was arrested by the Economic and Financial Commission (EFCC) on similar charges. In both cases, the bloggers were critical of the authorities.
African nations are far from alone in attempts to control the internet. However, stifling discourse as it emerges as a crucial medium on the continent poses worrying questions regarding freedom of speech.
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. You can follow BBC Monitoring on Twitter and Facebook.
As the mobile revolution continues to drive change across Africa, governments are rushing to introduce legislation to curb cyber crime and to regulate the use of social media platforms.