To announce the launch, Burger King released a video on April Fools' Day that shows unsuspecting Whopper fans eating the version with the Impossible Burger and then exclaiming that they can't taste the difference.

The Restaurant Brands International subsidiary is offering the Impossible Whopper at 59 St. Louis locations. The chain already sells veggie patties made by Kellogg's vegetarian brand, Morningstar Farms.

Burger King is testing a vegetarian version of its Whopper that uses an Impossible Burger for its patties, becoming the first national fast-food chain to sell the plant-based burger.

Silicon Valley-based Impossible Foods genetically engineers heme, a protein that makes the vegetarian-friendly burger taste like meat. The ingredient is also responsible for giving the patty red juices that make it look like it's bleeding, just like a piece of beef.

"We wanted to make sure we had something that lived up to the expectations of the Whopper," Burger King's North America president, Christopher Finazzo, told Reuters. "We've done sort of a blind taste test with our franchisees, with people in the office, with my partners on the executive team, and virtually nobody can tell the difference."

The Impossible Burger is already sold in more than 5,000 restaurants, but if Burger King takes it nationwide, it would more than double its footprint.

Impossible Foods spokeswoman Rachel Konrad told CNBC that the company is ramping up production at its manufacturing facility in Oakland, California to go from making 500,000 pounds per month to more than 2 million pounds per month. The company recently hired a second shift to help double production. She also said that they are expanding capacity further and looking beyond Oakland for more capacity.

The Impossible Whopper will cost about a dollar extra, but Finazzo said that research found that customers do not mind paying extra and like the plant-based burger for its health benefits.

Red Robin has also joined the ranks of fast casual restaurants bringing the plant-based burger to its 570 stores. Before Burger King's announcement, regional chain White Castle was the only fast-food restaurant to sell the Impossible Burger at its nearly 400 locations, which are mostly in the Midwest. Carl's Jr. launched a plant-based burger made in partnership with Impossible Food's main competitor, Beyond Meat.

Finazzo said that the company considered a Beyond Meat burger but chose Impossible Foods for the taste, brand recognition and price.

—Reuters contributed reporting to this story.