The engine was manufactured by CFM International, a joint venture of GE and France's Safran Aircraft Engines.
"The CFM situation right now is just so unfortunate. It's unfortunate that it happened. It couldn't have happened at a worse time for GE," Wright said on "Squawk on the Street."
Shares of GE, the Dow's worst performer, have fallen more than 21 percent year to date and over 54 percent in the last year. The company slashed its dividend in November for the second time since the Great Depression.
The Boston-based multinational is in the midst of restructuring. That could include splitting itself up into separate companies, with a decision announced as early as this spring. GE is scheduled to report first-quarter earnings before the bell Friday.
Southwest Flight 1380's engine failure adds to the negative news surrounding GE.
One passenger was killed when the engine's explosion caused shrapnel to cut into the Boeing 737-700's fuselage, blowing out a window. Passengers aboard the flight rushed to pull the victim back into the plane after she was partially sucked out of a window, witnesses said. The Dallas-bound flight made an emergency landing in Philadelphia.
An early review of the failed engine found preliminary evidence of metal fatigue where a fan blade had broken off, according to the U.S. National Transportation Safety Board.
The CFM56-7B, the type of engine involved in Tuesday's incident, is one of the most common in the world. It powers some 6,700 aircraft around the world, according to CFM International.
The Federal Aviation Administration sought more rigorous testing of the engine last August, when it proposed a rule that would subject the engines to ultrasonic tests of their fan blades. Late Wednesday, the FAA said it would issue a rule within two weeks requiring such tests.
Southwest late Tuesday said that it would accelerate testing of CFM56 engines "out of an abundance of caution." Several other airlines using this engine made similar announcements.
GE and Safran are deploying technicians to support Southwest's inspection program. "The members of the CFM Team worldwide wish to express their deepest condolences to family of the victim of this incident," CFM said in a statement.
— CNBC's Leslie Josephs contributed to this report.