Shake Shack (SHAK) - Get Report won't be going beyond offering traditional meat hamburgers anytime soon, ruling out the possibility of following in the footsteps of McDonald's (MCD) - Get Report , Restaurant Brands International's (QSR) - Get Report , Burger King and A&W, who have all introduced plant-based protein, meat-less burgers, the company's CEO said on Friday.

"We have no intention of doing it today," Shake Shack CEO Randy Garutti told CNBC's "Squawk Box " on Friday. "We want to watch and see how this plays out."

Garutti said that he was "fascinated" by the early sales numbers released by restaurants that have already introduced Beyond Meat (BYND) - Get Report meat-less patties, but that he wants to see if those numbers continue.

"Shake Shack was built on doing classic things better than other people did them, so let's watch a little bit," Garutti said.

Shares of Del Taco Restaurants (TACO) - Get Reportgained some positive attention this week following that company's announcement it will be adding two new burritos to its menu that use a new meatless faux-beef product being introduced by Beyond Meat.

Canada's Tim Horton's, another subsidiary of Restaurant Brands International, also recently announced that it is now offering faux-meat breakfast sandwiches made with Beyond Meat products at almost 4,000 of its locations. 

Shares of Beyond Meat were down 7.24% at $153.21 in trading Friday on the Nasdaq Stock Market. Shake Shack shares were down 0.25% at $67.15 on the New York Stock Exchange.