He said the firms had “unchecked power” to censure and edit the views of users.
President Trump has regularly accused platforms such as Twitter and Facebook of stifling conservative voices.
The order, which is expected to face legal challenges, comes after Twitter decided to append fact-check labels to two of his tweets this week.
On Wednesday Mr Trump accused the company of election interference after it added a warning label to the tweets about claims of widespread fraud in mail-in voting – also known as postal votes.
Twitter and other social media platforms strongly condemned the executive order.
And again, early this morning (Friday), Twitter hid one of President Trump’s tweets from his profile, saying it violates rules about glorifying violence.
