Rodgers described Mason's performance as "horrendous" and questioned whether the referee, who lives near Manchester, should have been selected for the match.
He said: "Hopefully we won't have a Greater Manchester referee with Liverpool-Manchester games in future."
In a statement, the FA said Rodgers' comments called into question the integrity of Mason and/or "implied that the match referee was motivated by bias".
Rodgers has until 1800 GMT on Wednesday to respond to the charge.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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