In this paper we define fuzzy congruences on $BCI$-algebras and their quotient algebras, and prove some fundamental results : \begin{enumerate} \item There is a one to one correspondence between the set $FC(X)$ of all fuzzy closed ideals of $X$ and the set $FCon_R (X)$ of all fuzzy regular congruences on $X$. \item Let $X,Y$ be $BCI$-algebras and $f : X \to Y$ be a $BCI$-homomorphism. If $\bar{A}$ is a fuzzy ideal of $Y$, then the quotient algebras $X/f^{-1}(\bar{A})$ and $f(X)/\bar{A}$ are $BCI$-algebras and $X/f^{-1}(\bar{A}) \cong f(X)/\bar{A}$ \end{enumerate}