Birmingham manager John Eustace said Etheridge was abused by fans after he celebrated his side's stoppage time equaliser in the 2-2 draw in the fourth round.
After the goal Etheridge went to referee Keith Stroud on the halfway line to complain about comments directed to him.
"Neil was racially abused at the end, which is bang out of order," Eustace told the BBC.
"There is no room at all in society, let alone football, for that."
Birmingham said they would assist the authorities while Blackburn issued a statement saying: "The club has a zero-tolerance policy for all forms of abuse and discrimination, and will take the strongest possible action against any individuals identified for committing such offences."
The FA said: "We are aware of an alleged incident of racial abuse that was reported to the match official.
"We take allegations of discrimination extremely seriously and we will be investigating as a matter of urgency."
