Peter Altmaier described the march of almost 700,000 as "deeply moving".
He also thanked those who participated in the march who asked for a "popular vote" in the final agreement with Brexit.
The economy minister wrote on Twitter: "The march of the popular vote is the most impressive and moving support for Europe that I have seen.
"Millions across Europe sit with you.
The Prime Minister of Scotland, Nicola Sturgeon, also showed her support with a video message.
She said: "Let me say this loud and clear, if the problem is presented before the House of Commons, the SNP parliamentarians will support a popular vote that includes the option of staying in the EU.
"The management of the conservative government of these negotiations has been chaotic, incompetent and ambiguous.
"Having spent two years telling us that" no agreement "was better than a bad deal, the Prime Minister is now preparing to pressure parliamentarians to vote for a bad deal or blindfolded, arguing that" no agreement "would be catastrophic.
"She is trying to scare the United Kingdom in the pan for fear of fire.
"It's a scandal and should not be accepted."
Chef Delia Smith argued that when people voted they were not fully informed about what they were voting for, but now they were beginning to understand "the terrible consequences."
She said: "The only way we can avoid total madness and recover our future has to be a popular vote."
While the EU has repeatedly stated that it would be open to the UK rejoining the EU should there be a second referendum, the Prime Minister has continuously rejected this idea.
She has repeatedly warned that a second referendum would be a total betrayal of the Brexit vote.