The grounding comes days before Boeing was due to deliver its first 737 MAX to an airline, and marks a high-profile delay in a program that Boeing had said was ahead of schedule.
It poses no safety concerns for travelers because no airlines are yet flying the 737 MAX, but it could mean a costly disruption if the problem persists. Timely delivery is important to planemakers as they get most of the payment for a plane when it is handed to the buyer.
Boeing shares fell 1.3 percent to $183.15 in afternoon trading on the New York Stock Exchange. GE shares were down 0.9 percent at $28.67.
Boeing said it still expects to deliver the first 737 MAX aircraft this month, and that production of both the MAX and current generation 737 will continue.
Safran found a quality problem in a disc used in the low-pressure turbine at the rear of the engine and notified Boeing over the weekend, Rick Kennedy, a spokesman for GE, said.
The 737 MAX replaces an older version of Boeing's best-selling single-aisle aircraft, a key moneymaker for the aerospace company.
Kennedy said the disc that prompted the concern had not been installed in an engine, but the discovery prompted Boeing to halt flights until engines could be inspected.
Safran received the disc from a supplier, but there are other suppliers of that part so production of the engine, known as the LEAP 1-B, was continuing, Kennedy said.
American Airlines Group Inc, which has 100 737 MAX jets on order, declined to comment and referred questions to Boeing. Southwest Airlines Co, the launch customer for the new aircraft, did not immediately respond to a request for comment.