Irish radio group Communicorp owns another Dublin station, 98FM, as well as national station Newstalk.
The BCI said: "The commission was not satisfied that Communicorp would not hold an undue amount of the communications media in the Dublin city and county franchise area following completion of this transaction [for FM104]."
Communicorp still needs approval from Ireland's Competition Authority to buy Highland Radio and Today FM, according to the BCI.
Communicorp is owned by Irish entrepreneur Denis O'Brien and has a portfolio of radio stations in Ireland and Central Europe.