“A relationship of violence acts upon a body or upon things; it forces, it bends, it breaks on the wheel, it destroys, or it closes the door on all possibilities. Its opposite pole can only be passivity, and if it comes up against any resistance, it has no other option but to try to minimize it. On the other hand, a power relationship can only be articulated on the basis of two elements which are each indispensable if it is really to be a power relationship: that “the other” (the one over whom power is exercised) be thoroughly recognized and maintained to the very end as a person who acts; and that, faced with a relationship of power, a whole field of responses, reactions, results, and possible inventions may open up.
Obviously the bringing into play of power relations does not exclude the use of violence any more than it does the obtaining of consent; no doubt the exercise of power can never do without one or the other, often both at the same time. But even though consensus and violence are the instruments or the results, they do not constitute the principle or the basic nature of power. The exercise of power can produce as much acceptance as may be wished for: it can pile up the dead and shelter itself behind whatever threats it can imagine. In itself the exercise of power is not violence; nor is it a consent which, implicitly, is renewable. It is a total structure of actions brought to bear upon possible actions; it incites, it induces, it seduces, it makes easier or more difficult; in the extreme it constrains or forbids absolutely; it is nevertheless always a way of acting upon an acting subject or acting subjects by virtue of their acting or being capable of action. A set of actions upon other actions.”
Michel Foucault, (2000)  ‘The Subject and Power’. In J. Faubion (ed.). Tr. Robert Hurley and others. Power The Essential Works of Michel Foucault 1954-1984. Volume Three. New York: New Press, p. 340-1
Random thoughts in response
As Frédéric Gros point out in his useful article Foucault – philosopher of violence? (2012), Foucault has little to say directly on violence per se. The above quotation is perhaps one of his most extended discussions on the topic. Earlier in a 1973 lecture after working through the notion, but not coming to an entirely satisfactory conclusion, he defines ‘violence [as] the physical exercise of a completely unbalanced force’. In the more refined argument he produces in ‘The Subject and Power’. Foucault argues that when violence is exerted it is no longer a power relation. Power relies on people willingly and freely agreeing to modify their behaviour (even if under extreme duress and threat). Power is about changing people’s actions – which is different from the simple act of destroying and exerting physical force on their bodies. Violence can certainly be used as an instrument of power to threaten people and the result of power can be violence, but the exercise of power is not in itself violence, just as power is not equivalent to knowledge.
Making this distinction can lead to interesting ways of conducting a nuanced discussion of the tensions between power and violence. One might discuss, for instance, how different people choose to respond in differing ways to acts of physical force. When violence is exercised the victim has no choice. In the exercise of power both sides have choices – even if these are restricted.
One could perhaps argue that the difference between power and violence is the issue of choice on both sides of the equation.
 Michel Foucault, Psychiatric Power: Lectures at the Collège de France 1973-1975. Edited by Jacques Lagrange. Translated by Graham Burchell (New York: Palgrave Macmillan, 2006), p. 14
With thanks to Steven Ogden for provoking these thoughts.