Does the Great Weapon Master feat grant wizards proficiency with heavy weapons?

Great Weapon Master does not grant any weapon proficiencies

As others have pointed out, the Great Weapon Master feat does not grant you proficiency with heavy weapons (which is to say, weapons with the "Heavy" weapon property, as per PHB. p 147) as nothing in the feat's description says that it does, but rather, the feat already assumes you have proficiency in a heavy weapon.

If you do not have proficiency with a heavy weapon already, then you are not able to make use of that second bullet point. You are, however, still able to make use of the first bullet point, since, as is discussed in this Q&A, you don't actually need to use a heavy weapon to benefit from that first bullet point, so a wizard with a dagger would still be able to benefit.

However, if you find another way to gain proficiency with a heavy weapon, you would be able to make use of that second bullet point. The most obvious ways to gain such a proficiency would be to multiclass; multiclassing into a class that gives you proficiency with all simple weapons would grant you proficiency with the Greatclub, which is a simple heavy weapon, but not a great choice; better is to multiclass into a class that grants martial weapon proficiency, such as barbarian, fighter, paladin, ranger, etc.

The other most obvious way to gain weapon proficiencies is via the Weapon Master feat, which gives you proficiency in any four weapons of your choice. If you chose at least one weapon that was heavy, such as a greatsword, then you would be able to use the second bullet point of Great Weapon Master (although that's quite the investment, using up two of your wizard's ASIs to gain those two feats).

For other ways to gain weapon proficiencies, see these related questions:

• Is there any way for my wizard to learn just sword proficiency?
• Weapon Proficiency without needing a particular class/race or multi-classing

No, the feat doesn't grant proficiency with any weapons

The description of the Great Weapon Master feat says (PHB, p. 167):

You’ve learned to put the weight of a weapon to your advantage, letting its momentum empower your strikes. You gain the following benefits:

• On your turn, when you score a critical hit with a melee weapon or reduce a creature to 0 hit points with one, you can make one melee weapon attack as a bonus action.

• Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack’s damage.

Nothing in the description of this feat says it gives the character proficiency with heavy weapons. The second bullet point is simply dependent on the character having heavy weapon proficiency before they can use that particular aspect of the feat.

If you're not proficient with a heavy weapon, you can't choose to take a -5 to the attack roll and add +10 to the damage, because you can't "make a melee attack with a heavy weapon that you are proficient with". You could still gain the first benefit if you crit or reduce a creature to 0 HP with any melee weapon.

Great Weapon Master does not grant any proficiencies.

First, if the feat granted proficiency with any weapons, it would state that it granted proficiency with a weapon. It does not.

Second, the clause you quote is defining the condition under which one may use the second bullet of the feat:

Before you make a melee attack with a heavy weapon that you are proficient with...

It states “before you make a melee attack”, then defines parameters for that melee attack, specifically, that it must be made with a heavy weapon you are proficient with. If you do not have proficiency with a particular heavy weapon, you may not use the second bullet of GWM while making attacks with that particular weapon.