"I have a lot of trouble with the valuation," said trader Tim Seymour.
Read MoreShake Shack shares jump on earnings beat
He called Jack in the Box a "much better story," adding that it is "improving and executing." Still, he noted the stock was not cheap at more than $90 per share.
In the restaurant chain space, trader Brian Kelly looked at El Pollo Loco. The stock has climbed 41 percent this year and closed Wednesday just above $28 per share. That company reports earnings Thursday afternoon.
But Shake Shack shares could have some value in the long term, trader Dan Nathan said. He noted that the chain has about 65 stores and room to grow.
Tim Seymour is long T, BAC, C, DIS, F, GE, GM, GOOGL, INTC, JCP, KO, SUNE, TBT and VIP. Tim's firm is long BABA, BIDU, CHL, DAL, MCD, NKE, NOK, SBUX and YHOO.
Dan Nathan is long SO, GOOGL June call fly, DDD Aug Calls, TWTR, WMT June call spread, BBRY June calls, QQQ May 108/ 98 put spread, IWM May put fly, XLP May put spread, XLY May puts, LULU May puts and INTC May /July put spread.
Brian Kelly is long BTC=, BBRY, SPY puts and U.S. dollar. He is short Australian dollar, yen and yuan.
Karen is long BABA, BAC, C, FINL, FL, GOOG, GOOGL, JPM, M, KORS and SEDG. She is short SPY. Her firm is long AAPL, ANTM, BAC, C, DIS, FBT, FINL, FL, GOOG, GOOGL, GPS, IBB, JPM, M, KORS, SUNE, URI and XBI. Her firm is short IWM, SPY, XRT and MDY. Karen Finerman is on the board of GrafTech International.