"This stock is so overvalued it's ridiculous," he said.
Shake Shack has still fallen nearly 20 percent in the last month. The stock, which late last month traded at less than half the value of its 52-week high, possibly rallied on short covering and remains "expensive," said trader Guy Adami.
Adami would instead look to struggling fast food behemoth McDonald's, which continues efforts to restructure and boost sales. The chain recently announced it would start serving all-day breakfast throughout the U.S. in October.
"Maybe this all-day breakfast thing will catch on and take it higher," Adami said.
Trader Tim Seymour, whose firm Triogem Asset Management owns McDonald's stock, said it has "a lot more room to run."
Tim Seymour is long AAPL, BAC, CLF, DIS, F, GE, GM, GOOGL, INTC, JPM, T, TWTR, Tim's firm is long BABA, BIDU, MCD, NKE, NOK, SBUX, YHOO.
Brian Kelly is long BBRY, GLD, TWTR calls, Bitcoin, U.S. Dollar, Crude Oil; he is short British Pound, Euro, Yen, Yuan, US Treasuries.
Guy Adami is long CELG, EXAS, INTC, Guy Adami's wife, Linda Snow, works at Merck.
Opinions expressed by David Seaburg are solely his own and do not reflect the views and opinions of Cowen Group Inc.