High wind power penetration presents many challenges to the flexibility and reliability of power system operation. In this environment, various demand response (DR) programs have received much attention. As an effective measure of DR programs, interruptible load (IL) programs have been widely used around the world. This paper addresses the concern of how the IL program impacts the equilibrium outcomes of electricity markets with wind power. First, a market demand model is developed to take consideration of the IL program. Next, a Cournot equilibrium model for electricity markets with an IL program and wind power is presented. The introduction of the IL program leads to a non-smooth equilibrium problem. To solve this equilibrium problem, a novel solution method is proposed. Finally, considering that wind power penetration will increase the risks faced by the conventional generators, the conditional value at risk is employed to measure the risk, so that the impact of the IL program on the generators’ risk can also be examined. Numerical examples are presented to verify the effectiveness of the method. It is shown that the IL program can lower market price and its volatility significantly. In addition, the IL program can help generators reduce their risks in the market, especially when the uncertainty in wind power output is relatively large.