First off I'm laughing at the responses who don't seem to know what functional programming is... or what languages restrict you to it. MOST languages now are at minimum hybrid, allowing for and using both.
JavaScript for example is NOT 'strictly' a functional language. EVERY variable type is an object with methods and properties. FUNCTIONS are in fact objects in JavaScript even when you're trying to use it as a functional/procedural language, meaning that JAVASCRIPT IS NOT A FUNCTIONAL LANGUAGE! No matter how much you may try to use it as such...
There are few if any truly "functional/procedural only" web languages and this is by design as the DOM (document object model) is an integral part of how HTML works and how you use it client-side. Server-side development therefore tends to follow this mode of thought as well.
Like you CAN use PHP as a functional/procedural language only, but you get into mysqli or PDO it's time to put on the big boy pants and use objects. Whilst sure, mysqli does have procedural wrappers for the object based functionality, those are exactly that -- WRAPPERS -- introducing uneccessary overhead and existing as little more than a crutch for the people migrating from mysql_ functions that cannot extract their head from ten years ago's rectum.
It is to that end that questing for a suitable "functional language" for web programming is a flawed concept, and whilst certainly possible (hell you could use vanilla C or Pascal if you wanted) it is NOT something I would recommend.
Man up and learn to use objects! Just don't go overboard and use them for EVERYTHING -- that's where IMHO a lot of languages (Java for example) go bits up face-down as they try to shoe-horn everything into that model, and the result is often less than desirable.
Functions/procedures handle static tasks extremely well, particularly in places where you can pass by reference or handle multiple data types off one call. Objects shine for restricting scope whilst retaining values, creating pointered lists, and a host of other specific uses.
Each has their place, and that's why so far as I'm concerned the better languages allow for BOTH! Restricting yourself to one or the other is a pointless restriction.