We consider the problem of linear transceiver design to achieve max-min fairness in a MIMO interfering broadcast channel (IBC). This problem can be formulated as maximizing the minimum rate utility subject to a set of per-BS transmission power constraints. The considered problem is intrinsically very difficult, as differently from the popular weighted sum rate maximization problem, the min rate utility is non- differentiable. Moreover, our analysis indicates that when the number of antennas is at least two at each of the transmitters and the receivers, the max-min utility maximization problem is NP-hard in the number of users. As a result, we develop a low-complexity algorithm that computes an approximate solution to the max-min utility optimization problem. Numerical results show that proposed algorithm is efficient in achieving fairness among all the users.