Used in hand--to--hand combat, a melee 
Attack allows you to 
Attack a foe within your reach. A melee 
Attack typically uses a handheld weapon such as a sword, a 
Warhammer, or an axe. A typical monster makes a melee 
Attack when it strikes with its claws, horns, teeth, 
Tentacles, or other body part. A few 
Spells also involve making a melee 
Attack.
Most 
Creatures have a 5-foot 
reach and can thus 
Attack Targets within 5 feet of them when making a melee 
Attack. Certain 
Creatures (typically those larger than Medium) have melee 
Attacks with a greater reach than 5 feet, as noted in their descriptions.
Instead of using a weapon to make a melee weapon 
Attack, you can use an 
Unarmed strike: a punch, kick, head--butt, or similar forceful blow (none of which count as weapons). On a hit, an 
Unarmed strike deals bludgeoning damage equal to 1 + your 
Strength modifier. You are proficient with your 
Unarmed strikes.
from 
https://www.google.com/url?sa=t&rct...elee_Attacks&usg=AOvVaw1xifz1OvvVS73NSbzn0XF_
your magic weapon seems to follow all the requirements so far.