Ok, So this has been bugging me for quite some time because even though the solutions above do work, they didn't do exactly what I needed, maybe this solution will help you.
Basically, I had 2 types of variable products in the store: One where the weight (and therefore price) changed, and the other where only the flavour changed (and therefore not the price). The problem with setting the From price to display: none is that on the fixed price (but variable flavour) the price would disappear too. So I needed some way to remove the price only if it said From before it. For me, the easiest solution was jQuery:
$from = $('.summary').find('.from');
If you have a valid js using jquery file, placing the above code in it removes the from text and the from price only if it is on a page where the from text would be visible. The reason I use the $('.summary') is to ensure it removes it only from within the single product description :
Hope this helps somebody!