Shake Shack shares rose more than 12 percent on Friday alone, closing above $68. The next big mover for Shake Shack comes on Aug. 10, when it reports quarterly earnings.
Kelly also noted that recent momentum could drive McDonald's shares higher. The stock has climbed more than 1 percent since the struggling fast food giant's mixed results last week.
"Earnings weren't spectacular, but people are starting to believe the turnaround story," said trader Guy Adami, who agreed that the stock could grind higher.
Trader Tim Seymour—who owns McDonald's stock—said management is "getting there" with driving change and moving to increase profitability.
Tim Seymour is long AAPL, T, BAC, DIS, F, GE, GM, GOOGL, INTC, JPM, SUNE, Tim's firm is long BABA, BIDU, MCD, NKE, NOK, SBUX, YHOO.
Brian Kelly is long BBRY, BTC=; ITB, TAN, TLT, TSL, US dollar; he is short Oil, Ruble, Yuan and Yen.
Guy Adami is long CELG, EXAS, INTC, Guy Adami's wife, Linda Snow, works at Merck.