Many investors and analysts have called for a change amid a sluggish run for Twitter's stock. The company has struggled to expand its user base and grow revenue through advertising and other streams. But Dorsey said in a conference call Thursday that Costolo's departure did not reflect the company's near-term results.
Read MoreAfter CEO exit, Twitter says no strategy change
Still, traders felt the stock has room to climb higher; it closed Thursday below $36 per share. Investors should stay long in the stock using $35 as a stop, trader Guy Adami said.
Twitter will likely rise during Dorsey's interim tenure, trader Brian Kelly added. Trader Dan Nathan—who owns Twitter stock—said he would stick with the name.
Adami added that regardless of whether Facebook will see a flood of advertisers or other business after Twitter's shake-up, it stands to move higher. The stock closed Thursday just below $82 per share.
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Brian Kelly is long DXGE, BTC=, BBRY, U.S. dollar and oil. He is short Australian dollar, Canadian dollar, euro, yen and yuan. Today he entered into short euro. Today he closed out his short U.S. 30-year bonds and short DAX.
Dan is long SPY June put fly, TWTR, BBRY June calls, SO, DE June put fly, INTC July put, WMT June call fly, LVS July Aug put spread, TWTR Sept call spread, GRRO June put fly and CAT July/August put spread. He is short SO Aug calls. Today, he bought CAT July/August put spreads.
Karen is long BABA, BAC, C, FINL, FL, GOOG, GOOGL, JPM, KORS, M and URI. She is short SPY. Her firm is long ANTM, AAPL, BAC, C, DIS, FBT, FINL, FL, GOOG, GOOGL, GPS, IBB, JPM, KORS, M, SUNE, URI, XBI, KORS calls, URI calls and SPY puts. Her firm is short IWM, SPY, MDY and M calls. Karen Finerman is on the board of GrafTech International.
Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.