While the restaurant industry has been reeling under a demand slowdown spurred by cautious consumer spending, Shake Shack's relatively upscale offerings and marketing initiatives have helped buck the trend.

"If you market something right, you see change happening," Conzo said.

He notes Shake Shack has gotten "very creative with their menu," adding "crinkle cut fries" and "a spicy burger."

"Shake Shack is doing a great job marketing their new items, driving traffic as opposed to, let's say a Wendy's," Conzo said.

Fast-food industry traffic declined 1.6% in the fourth quarter, according to data from Placer.ai, with major names including McDonald's and Taco Bell also seeing weaker store visits.