The aircraft will not fly until a software update can be tested and installed, the US regulator said.
Sunday's crash, shortly after take-off from Addis Ababa, killed 157 people from 35 nations.
It was the second crash involving a 737 Max in six months.
Some people have pointed to similarities between the incidents, with some experts citing satellite data and evidence from the crash scene as showing links between Sunday's disaster and October's crash in Indonesia of the Lion Air jet that killed 189 people.
US Representative Rick Larsen said the software upgrade would take a few weeks to complete, and installing it on all the aircraft would take "at least through April".
The FAA said on Wednesday that a software fix for the 737 Max that Boeing had been working on since the Lion Air crash would take months to complete.
Meanwhile, investigators in France have taken charge of the crashed Ethiopian Airlines aircraft's black boxes as they attempt to uncover what caused the Boeing 737 Max disaster.
The Bureau of Enquiry and Analysis for Civil Aviation Safety (BEA) received the flight data and cockpit voice recorders on Thursday.
The first readings could take days, but a lot depends on the boxes' condition.
Regulators across the world continue to ground the Boeing aircraft.
On Thursday, Russia, Japan and Tunisia banned the jet from their airspace. Late on Wednesday, the FAA told the country's airlines to ground their fleets, but was criticised for not doing it sooner.