The pilot said the anti-stall system was making it hard to control the plane in a flight simulator - telling a colleague in 2016, "Granted, I suck at flying, but even this was egregious", the New York Times reported Friday.
"The FAA finds the substance of the document concerning", the regulator said in a statement.
"I understand that Boeing discovered the document in its files months ago", Dickson said.
A lawyer representing Boeing in the matter, McGuireWoods LLC's Richard Cullen, said in a statement that: "The Boeing Company timely produced the Mark Forkner IM document to the appropriate authorities".
In a letter to Boeing chief Dennis Muilenburg, FAA Administrator Steve Dickson said: "Last night, I reviewed a concerning document that Boeing provided late yesterday to the Department of Transportation".
In the exchange, Forkner said he was writing while "drinking icy cold grey goose".
Forkner responded soon after: "Granted I suck at flying, but even this was egregious".
The Seattle Times reported in September that Forkner repeatedly invoked his Fifth Amendment right to not turn over documents subpoenaed by the justice department.
The messages appear to be the first publicly known observations that MCAS behaved erratically during testing before the aircraft entered service.
Boeing shares tumbled 5% on the disclosure of the communications that the FAA had been unaware of.
Boeing is now revising the 737 MAX software to add more safeguards and require the MCAS system to receive input from two key sensors.
The 737 MAX was Boeing's most popular narrow-body passenger jet, used by major U.S. airlines and around the world.
Boeing turned over the transcript to the Justice Department earlier this year gave it to Congress only this week in anticipation of Muilenburg's scheduled October 30 testimony before DeFazio's committee, according to a person familiar with the matter.
Southwest, which on Thursday delayed the return of the plane to its schedule until February, said on Friday it was unaware of the internal messages but continued to work with Boeing and the FAA "in their shared pursuit of safety". While Boeing "has always said safety is Number One ... the question is that just something they took for granted, that they paid lip service when the real Number One was let's make this plane as cheaply as possible and with minimum changes for the airlines to get what they want".
Boeing shares fell after Reuters reported on the FAA's comments earlier Friday.