The Doha-based news network said its service provider prevented the attackers from gaining access to their platforms.
In a statement on Wednesday, Al Jazeera said that "continued electronic attacks aimed at accessing, disrupting and controlling some of the news platforms" between Saturday and Tuesday.
"Al Jazeera's service provider was able to monitor and fend off all the hacking attacks and prevent them from achieving their goal," the statement added.
The Qatari-funded broadcaster said the attacks reached their height on Sunday, ahead of the documentary on Hamas-Israel negotiations on its Arabic-language channel. The documentary contained an audio recording said to be the voice of an Israeli captive.
In the recording, the man says he is "an Israeli soldier held captive" by the Islamist group.
The Israeli military has said it is investigating the clip.
Al Jazeera, which has been censored and banned by several Middle Eastern regimes, has been targeted by hackers in the past, including during the Gulf diplomatic crisis of 2017.
As the rift broke out in June of that year, Al Jazeera fended off a large-scale cyberattack following a successful hack of Qatar's official Qatar News Agency.