The Hardball host told viewers that if Sanders became the Democratic nominee, Republicans would release opposition research about "what [Sanders has] said in the past about world affairs, how far left he is," which would "kill him" in the general election in November.
"But I think it's a little late to stop him," Matthews told viewers.
Then the MSNBC star turned to the history books for an analogy to describe his feelings at watching a series of top Democrats be outpaced by Sanders.
"I was reading last night about the fall of France in the summer of 1940," said Matthews, "And the general, Reynaud, calls up Churchill and says, 'It's over.' And Churchill says, 'How can that be? You've got the greatest army in Europe. How can it be over?' He said, 'It's over.'"
Matthews added, "So I had that suppressed feeling."
The comment prompted outcry not just from Sanders' supporters; many people on Twitter described the reference to a Nazi invasion to discuss a prominent Jewish candidate as distasteful.
A spokesperson for MSNBC didn't immediately respond to a request for comment about what Matthews said.
But Mike Casca, communications director for the Sanders campaign, responded on Twitter.
"Never thought part of my job would be pleading with a national news network to stop likening the campaign of a Jewish presidential candidate whose family was wiped out by the Nazis to the Third Reich," he wrote. "But here we are."
On Monday, Matthews apologized during his show and vowed to do better as the campaign continued.
"Sen. Sanders, I'm sorry for comparing anything from that tragic era, in which so many suffered, especially the Jewish people, to an electoral result in which you were the well-deserved winner," he said.
Matthews is not the first MSNBC anchor to be criticized for using allusions to the Nazis when discussing Sanders. Earlier this month, Chuck Todd quoted an article on air from a conservative writer that described some of Sanders' supporters as a "digital brownshirt brigade."
In a post-debate show earlier in February, Matthews also began discussing Cold War executions when speaking of Sanders' embrace of democratic socialism.
"I believe if [Fidel] Castro and the Reds had won the Cold War, there would have been executions in Central Park and I might have been one of the ones getting executed. And certain other people would be there cheering, okay?” said Matthews.
"So, I have a problem with people who take the other side. I don’t know who Bernie supports over these years,” he added. “I don’t know what he means by 'socialist.'"