The hashtag #DataMustFall has been trending nationwide on social media over the past 24 hours.
This is despite South Africa having the most affordable mobile internet in Africa, according to the International Telecommunication Union.
The hashtag is a play on other campaigns such as #RhodesMustFall.
This was a call to topple a statue of colonialist Cecil Rhodes.
It was followed by a campaign against President Jacob Zuma - #ZumaMustFall.
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Around three in 10 people in Africa have access to the internet.
The continent lags behind average global internet penetration, which is just under 50%.
Although South African internet costs are low compared to the rest of Africa, it ranks 66th in global terms.
How much does mobile data cost? (500 MB prepaid mobile data)
Source: Measuring the Information Society Report, ITU (2015)
Radio personality Thabo Molefe, who started the campaign, says that a drop in prices would enable students to access online learning materials:
"Young people should be able to enjoy the benefits of e-learning by downloading textbooks online or catching up on a lecture on YouTube, but they can't do that because everything revolves around data and WiFi," he tweeted.
The parliamentary committee for telecommunications has decided to hold public hearings over the cost of high-speed internet following the outcry.
The online campaign has resonated with many people in South Africa, who took to Twitter to voice their frustration with what they say are overpriced data packages.
Local unions and the opposition Economic Freedom Fighters have rallied behind the calls the reduce internet prices.
A campaign has been launched in South Africa calling for telecom providers to reduce how much they charge for internet services.