A Russian group called New World Hackers claims it took down the website, telling the BBC it was done “in protest” against Gabon, the host of this year’s Africa Cup of Nations.
“Gabon is a country of dictatorship,” a member of the group told BBC Sport.
Caf has added a five-second process that screens all visitors, called a Cloudflare, to alleviate the problem.
“Caf has taken action but we can’t certify 100% it will not happen again,” Junior Binyam, the governing body’s communications director, told BBC Sport.
“Even CIA servers are hacked.”
The African football body’s website was shut down for around five hours on Saturday, leading officials from African football’s ruling body to investigate a technical fault prior to deciding the issue lay elsewhere.
This year’s Nations Cup has been the subject of opposition from a section of Gabonese who have used it as a vehicle to express political grievances.
Following last year’s disputed presidential elections, won by the incumbent Ali Bongo (who originally took power in 2009), people took to the street in protest.
The Gabonese authorities say three people died following violent clashes, while the opposition – led by former African Union chair Jean Ping – said the death toll was much higher.
In the ensuing months, the opposition called for a boycott of this year’s football tournament, which – having started on 14 January – will end on 5 February.
On Sunday, the New World Hackers also claimed to have taken down the website of oil company Total, which signed a multi-million dollar sponsorship deal with Caf last year.
“I don’t want to talk a lot but yes, we did the same to Total,” the New World Hackers member, who requested anonymity, told the BBC via email.
The BBC has reached out to Total for comment but has yet to hear back.
On Sunday, Gabon became the first Nations Cup hosts in 23 years to be eliminated in the group stage of a Nations Cup following a limp goalless draw against cameroon.
