Twitter, Facebook and Instagram blocked the president's accounts from their sites in the aftermath of the storming of the US Capitol by his supporters on Wednesday.
Speaking to Sky News' Sophy Ridge on Sunday programme, Mr Hancock, the UK health secretary and former culture secretary, said the move "raises a very important question" about social media companies "taking editorial decisions".
He said: "I think it raises a very important question, which is it means that the social media platforms are taking editorial decisions.
"And that is a very big question because then it raises questions about their editorial judgments and the way that they're regulated.
"It is obviously one for the culture secretary – but as a former culture secretary I can tell you that I think it does lead to very interesting questions about the role of social media and the role of the social media companies in the decisions, in the editorial decisions that they take."
Speaking later to the BBC's Andrew Marr show, Mr Hancock said: "The scenes, clearly encouraged by President Trump – the scenes at the Capitol – were terrible – and I was very sad to see that because American democracy is such a proud thing.
"But there's something else that has changed, which is that social media platforms are making editorial decisions now.
"That's clear because they're choosing who should and shouldn't have a voice on their platform.
"Now I think we should just be straightforward about that. Now that has consequences and they're very much – as you say – for the Culture Department and not for me."
Mr Trump was expected to travel to the US-Mexico border on Tuesday to highlight his administration's work on the border wall, the White House has said.
The visit will likely be the president's first public appearance since he addressed supporters on Wednesday, riling up a crowd that later staged a violent siege of the US Capitol. He is anxious to highlight accomplishments as his presidency winds down.