EDIT: I'm really talking about the Macedonian-style phalanx as in that which Phillip and Alexander utilised, I know the phalanx changed during the Hellenistic period and the flexibility of the army around the phalanx probably changed for the worse.

That the Macedonian-style phalanx did this as a result of tight formation and long, strong pikes is a bit of a mainstay in ancient military history, but common sense has to be applied.

A key contemporary source for this claim is Polybius,and [u]saltandvinegarrr gives a nice summary of that. I'm sure an expert on Hellenistic warfare could provide better sources, but even authoritative sources mention that the Hellenistic phalanx could block missiles (Serrati 183). Lendon (121-3) is a serious expert, and while he provides a nice diagram he doesn't mention missile-blocking. Funnily, I also couldn't find any such reference in the Cambridge History of Greek and Roman Warfare. But I have heard it in other places and I find it believable, I certainly can't think of it being explicitly denied anywhere.

I think this is an issue that most historians view as probably being the case but not an important aspect of the Macedonian-style phalanx's function. So I'm going to apply common sense here. Firstly, the Macedonian army was a combined arms unit, and so a phalanx was not expected to stand there and suffer heavy missile fire with no response from his fellow soldiers. Alexander utilised offensive action to pressure his missile-heavy Eastern opponents (Arrian has Alexander always rushing to the attack, Herodotus has the Athenians do similar at Marathon), had plenty of his own ranged troops, and later in his career also included large numbers of archers not only in his army but incorporated them into the phalanx itself. So the phalanx had other defences against missile fire aside from physical protection in the form of the various moving parts of the army fulfilling their separate roles.

Looking at the physical spacing and equipment of the sarissaphoroi gives us other clues. They all had helmets, but only the front five ranks (ie. the ones doing the fighting) had body armour. They all had shields strapped to their left arms. As [u]saltandvinegarrr pointed out, the back ranks had to hold their spears up anyway for reasons of safety, space and retaining the ability to manoeuvre. And as also stated, looking at a diagram of the Macedonian phalanx you can see how the hedge of pikes could block missiles. The fact that the troops at the back did not have body armour but did still have shields shows that while they were not expected to engage in a lot of direct fighting, they could still protect themselves against missiles. Note that these phalangites stood about 18 inches apart (Phang, 54-5), and so there was lots of space between each man that a missile could still slip through. So the pikes themselves were only partial protection, and the rest of their protection came from helmets, shields, the actions of the army's other supporting elements, and offensive action on the part of the phalangites.

To summarise, I think the Macedonian phalanx was quite clearly capable of blocking missiles, but it was far from missile-proof. Like any heavy infantry (even the Romans, whose infantry were highly vulnerable to horse archery), heavy missile fire was a vulnerability that was countered by a combination of heavy equipment and support from other elements of the army.

Sources:

Arrian, Herodotus, Polybius

Lendon, Soldiers and Ghosts, 121-3

Phang, Roman Military Service: Ideologies of Discipline in the Late Republic and Early Principate, 2008, 54-5.

Sekunda, Sabin and De Souza from Cambridge History of Greek and Roman Warfare, 2008

Serrati from The Oxford Handbook of Warfare in the Classical World, 2013, 183