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Brighton's third-round clash with Crystal Palace on January 8 has been selected for the trial of the technology, otherwise known as VAR, which is also to be used in selected fixtures throughout the rest of the competition.
The VAR is currently being used in Italy and Germany and was employed for the first time in an official game in Britain during the international friendly between England and Germany in November, when it was not called on.
"The FA has always been open to trialling new innovations and was heavily involved in the advancement of goal-line technology before it was introduced," said the FA's director of professional game relations Andy Ambler.
The trials in Britain will also include January's League Cup semi-finals.
Last year the International Football Association Board approved a two-year trialling of the VAR system.
The FA confirmed in its statement that the technology will only be employed to counteract "clear and obvious errors" on specific incidents in three situations: goals, penalty decisions and straight red cards or mistaken identity for red or yellow cards.
The VAR will automatically check every relevant incident and will inform the referee of any clear and obvious error.
The referee then has the power to change the original decision based on the new information provided by the VAR, or watch a replay on the side of the pitch.
