A regex splitting on word boundary \b isn't the best solution for this:

var prefix = "prefix";
var classes = el.className.split(" ").filter(function(c) {
    return c.lastIndexOf(prefix, 0) !== 0;
});
el.className = classes.join(" ").trim();

or as a jQuery mixin:

$.fn.removeClassPrefix = function(prefix) {
    this.each(function(i, el) {
        var classes = el.className.split(" ").filter(function(c) {
            return c.lastIndexOf(prefix, 0) !== 0;
        });
        el.className = $.trim(classes.join(" "));
    });
    return this;
};

2018 ES6 Update:

const prefix = "prefix";
const classes = el.className.split(" ").filter(c => !c.startsWith(prefix));
el.className = classes.join(" ").trim();