The President accused the company of targeting his supporters by making their posts harder or impossible to find.
Twitter denied "shadow banning" anyone but the President's intervention saw shares crash by three per cent this morning.
President Trump wrote: "Twitter SHADOW BANNING prominent Republicans. Not good.
"We will look into this discriminatory and illegal practice at once! Many complaints."
Celebrity backers like Hollywood actor James Wood called on investors in Twitter to pull out their cash.
He wrote: "I urge every @Twitter user who has had an account shadow banned to sell all stock holdings in @Twitter.
"Hit these creeps in their stock value. It’s the only way to fight this bias.
"We fought @facebook (stock down) and @CNN (ratings down) and won. It works! @Twitter next."
Trump's tweet followed a Vice news report on Wednesday that big-name Republicans including Donald Trump Jr's spokesman were being "shadow banned."
And James O'Keefe from Trump-backing news site Project Veritas posted undercover videos alleging to show Twitter engineers being caught red-handed admitting that shadow banning was commonplace.
Twitter wars: What is ‘shadow banning’?
This means that their tweets would still be viewable on a timeline to themselves, but not to other people even via a search.
Twitter users wishing to see a silenced user's tweets would need to know the exact handle they are searching and would have to go directly to their profile.
The idea of this is to limit the user’s reach on the platform, without them being aware that they have been silenced.
In one clip a man named as Abhinav Vadrevu, a former software engineer, says: "It's a lot of bad press if, like, people figure out that you're like shadow banning them.
"It's like, unethical in some way."
The White House did not specify if an investigation into Twitter would be launched or how such a probe would be carried out.
Twitter's shares were already lower in pre-market trading today after social media rival Facebook last night posted lower earnings than expected.
Twitter did not comment directly on Trump's tweet but said in a statement it does not "shadow ban."
It said: "We are aware that some accounts are not automatically populating in our search box, and we're shipping a change to address this".
Twitter added that the technology used is based on user behaviour rather than political views.
Twitter's senior strategist Nick Pickles told US lawmakers last week that the company does not discriminate based on politics.
He told the US House of Representatives Judiciary Committee: "Our purpose is to serve the conversation, not to make value judgements on personal beliefs".
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