Deeney and several fans reported hearing the abuse after Tuesday's 2-0 defeat by Cardiff as the players left the pitch.
"Blues gives its full support to Troy and is appalled and saddened that yet again, one of our players is not safe from discrimination on the football pitch," Birmingham said in a statement on Wednesday.
"The club captain and those inside St Andrew’s identified this as coming from the home section of the Gil Merrick lower when players were leaving the field of play towards the players’ tunnel.
"This incident has been referred to the relevant authorities and the club will assist in their investigation.
"There is no place for racism in the game."
Deeney joined his hometown club in 2021 and has made 53 appearances for Birmingham, scoring six goals this season.
