Chambers is ill so he and lightweight pair team-mate Will Fletcher will be absent from the event in Poland.
Illness has also affected GB's women's quadruple sculls team so Nixon, Bethany Bryan, Mathilda Hodgkins-Byrne and Jess Leyden will not be in action.
Rebecca Shorten will compete in the women's eight with Joel Cassells in the lightweight pair.
After winning gold in the opening World Cup regatta in Belgrade in early May, Chambers and Fletcher finished a disappointing sixth in the European Championships three weeks later.
Nixon and her British team-mates did clinch bronze at the European Championships with Shorten and Cassells' boats having to be content with fourth-place finishes.
Northern Ireland rowers Peter Chambers and Holly Nixon will both miss this weekend's World Cup regatta in Poznan.