Malik announced the government's plan to lift the ban on YouTube and Twitter on Friday night.
"I chaired a high level (meeting with) all stakeholders on the (YouTube). (Good) job by PTA (to) block anti-Islamic material! (Please expect YouTube) unblocked in 24 hrs," he said in a tweet.
He acknowledged in another tweet that there was a "great demand to unblock (YouTube) from all sections of society", especially users of Twitter.
"Expect the notification today! Hope u r all happy now," he said.
Prime Minister Raja Pervez Ashraf had in mid-September directed authorities to block YouTube for hosting "blasphemous material", including clips from the movie 'Innocence Of Muslims'.
The film triggered violent protests by right wing groups across Pakistan and the government itself sanctioned a day of protests on September 21, which was observed as "Love the Prophet Day".
Twenty-three people were killed and property worth billions of rupees was destroyed during these protests.
The Express Tribune newspaper criticised the government for continuing with the ban on YouTube in an editorial on Friday.
"The original excuse for the ban - that the website was hosting an anti-Islam video - can no longer be the justification given that few even remember anything about the video now," said the editorial that marked the ban entering its 100th day.
"This is purely a naked power play by the government and one that we should resist. This is about controlling our behaviour and denying us access to the internet.
This is about the only logical explanation left since YouTube has millions of videos of which a bare handful would be considered objectionable by the government and the judiciary," it said.
The editorial said the government should realise that it is not possible to censor the internet "the way that governments used to censor media in the print age".
A proposal to build a firewall like China, where the internet would be controlled by the government, too is "extremely worrying".
Regressing to a "dark age when a centralised authority controlled all access to information" would "essentially mean that we were longer living in a democracy", it said.