vue.js and jQuery can be complementary or unique depending on what you want to do.
But in general the answer is if you use vue.js then you do not need jQuery.
The concept behind modern libraries such as vue.js or React.js is to have built-in mechanisms for redrawing the page and content. This type of "work" was typically done by libraries like MooTools or jQuery. So without the need for such tools what happens is that old libraries fall into disuse.
If you have some functionality that vue.js does not do (eg AJAX requirment, or a specific jQuery plugin) then you can use jQuery. If not, then you no longer need jQuery.
Note that if you use jQuery you probably have to insert through compiler like webpack or browserify . I found one for the webpack and one for the browserify , but that's a separate question.