The rules for improvised weapons state that you can throw a melee weapon even if it does not have the thrown property for 1d4 damage:
If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage.
It is also stated that using an improvised weapon when it is similar to an existing weapon allows one to add their proficiency bonus to the attack:
At the GM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus,
Does this mean that when throwing a weapon this way, if a character is proficient with the weapon being thrown they get to add their proficiency bonus to this attack?
(The character does not have the Tavern Brawler feat which would make this trivial. This question asked in regards to a discussion on this homebrew question)
Best Answer
Only if you are ruled as using an improvised version of a proficient weapon
The relevant piece of information, PHB p. 147:
If you use an object that's similar to a weapon as if it were that weapon, that assumes you're using the weapon it was intended, with all of the applicable damage types, proficiencies, and properties associated with it.
Alternatively, if you use an object that bears no resemblance to a weapon, the object can deal 1d4 damage and the Thrown property.
However, you cannot use an object that's similar to a weapon and use it as if it were that weapon, and still have the object be something that bears no resemblance to a weapon.
If you attempt to throw a weapon without the thrown feature, you are no longer using the weapon the way it was intended, and it has to be treated as a different weapon. If a different weapon is applicable, use the new weapon's properties and proficiencies. Otherwise, treat it as an Improvised Weapon, with the applicable properties and proficiency.
With this information, you effectively have two choices:
Have your DM treat the original weapon as a second, different weapon that has the Thrown feature. Example: treating a Halfling's War Hammer (no Thrown) as a Goliath's Light Hammer (with Thrown).
Make your attack as using an Improvised Weapon, dealing 1d4 damage and using the default thrown option of 20/60 range, and only adding proficiency if provided by another feature (as from Kensei or Tavern Brawler)