Lopez Obrador stated that the move provided a hindrance to freedom of speech in a press briefing on Friday.
"How can you censor someone? Let’s see, I, as the judge of the Holy Inquisition, will punish you because I think what you’re saying is harmful?" he remarked. "Where is the law, where is the regulation, what are the norms? This is an issue of government. This is not an issue for private companies."
In a statement later that same day, spokesman Jesus Ramirez wrote: "Facebook’s decision to silence the current leader of the United States calls for a debate on freedom of expression, the free exchange of information on the web, democracy and the role of the companies that administer [social] networks."
On Friday, Twitter made the decision to suspend Trump permanently from its platform. In doing so, they wrote: "After close review of recent Tweets from the @realDonaldTrump account and the context around them — specifically how they are being received and interpreted on and off Twitter — we have permanently suspended the account due to the risk of further incitement of violence. "
The action was the most sweeping punishment any major social media company has ever taken against Trump, who has used his Twitter account to announce White House policy, attack rivals and widely disseminate misinformation.
For years, Twitter has been under pressure from critics to limit the reach of Trump's falsehood-laced tweets. Calls for Trump to be banned from Twitter have also been long mounting.
Yet officials at Twitter stood by his account, since the platform generally gives wide berth to accounts from world leaders whose posts have public value.
That all changed following the violent riots that overtook the Capitol earlier this week after a deluge of posts attempting to sabotage the result of the presidential election.
Now, @realDonaldTrump is gone for good and attempts to evade the ban will result in enforcement, Twitter officials warn.
"After close review of recent Tweets from the @realDonaldTrump account and the context around them — specifically how they are being received and interpreted on and off Twitter — we have permanently suspended the account due to the risk of further incitement of violence," the company said in a statement.
Facebook and Instagram will also not allow the president to post from his account for the remainder of his term and perhaps "indefinitely," according to the company's CEO Mark Zuckerberg.
"We believe the risks of allowing the president to continue to use our service during this period are simply too great," he said. "Therefore, we are extending the block we have placed on his Facebook and Instagram accounts indefinitely and for at least the next two weeks until the peaceful transition of power is complete."