A preliminary report of the Lion Air crash also showed that the pilots fought with the automatic safety system, known as the maneuvering characteristics augmentation system (MCAS), for control of the jet.
The FAA also did not delve in detailed inquiries and followed a standard certification process on the MAX, the paper said, citing an FAA spokesman.
Ethiopian Airlines has offered the relatives of 157 victims of last Sunday's Boeing 737 Max plane crash bags of scorched earth to bury in place of their loved ones, reports say.
Transport Minister Dagmawit Moges said on Sunday that flight data from the Ethiopian airways black boxes suggested strong parallels with a crash off Indonesia last October.
The manufacturer said Sunday it was close to releasing a long-awaited software patch to the system. The subpoena listed a prosecutor from the Justice Department's criminal division as a contact, according to the Journal.
The Journal said the probe would zero in on Seattle-area FAA offices.
Boeing's main rival Airbus has seen its stock rise 5 percent since the crash, but can not simply pick up the slack given the complicated logistics of plane-building.
With the prestige of one of the United States' biggest exporters at stake, Boeing has said the MAX series is safe, although it plans to roll out new software upgrades in days.
According to engineers who worked on the system, Boeing's own analysis of the safety system had several crucial flaws, including underestimating the power of the system to control the horizontal tail to push the nose down to avert a stall.
The FAA granted the aircraft airworthiness certificates and must now decide whether to withdraw them. "This change disrupted the plane's center of gravity and caused the Max to have a tendency to tip its nose upward during flight, increasing the likelihood of a stall", Zhang said.
"The FAA considered the final configuration and operating parameters of MCAS during MAX certification, and concluded that it met all certification and regulatory requirements", Boeing added.
It said, without elaborating, that there had been "some significant mischaracterisations" of the certification process.
Michel Merluzeau, an analyst at AirInsight, urged a cautious process.
Regulators across the world have banned the Boeing 737 Max from using airports or flying across their airspace due to concerns about passenger safety. "And, the global system of aircraft certification reciprocity is at risk too", he said.