Herzog, the wife of President Isaac Herzog, met Zelenska at the coronation of England's King Charles III earlier this year.
Ukraine is an important global grain and oilseeds producer, but its exports have fallen significantly since Russia's full-scale invasion in February 2022.
Ukraine and Russia blame each other for the dam's destruction, which has sent floodwaters across a war zone and forced thousands to flee.
Oleksiy Danilov, Secretary of Ukraine's National Security and Defense Council, dismissed statements by Russian officials who have said the counteroffensive has already begun.
A Ukrainian military spokesperson said Russia's aim was to prevent Ukrainian troops crossing the Dnipro River to attack Russian occupying forces.
What is the dam and what happened - and what do we not know?
The woman, said to be over 80 years old, was injured in Russian shelling that killed a Ukrainian mother and daughter on Thursday.