Using the commands:

 /scoreboard players set @a Rupees 1 {Inventory:[{Count:1b,tag:{display:{Name:"Rupee"}}}]}

or

 /scoreboard players set @a Rupees 2 {Inventory:[{Count:2b,tag:{display:{Name:"Rupee"}}}]}

does work,

 /scoreboard players set @a Rupees 0 {Inventory:[{Count:0b,tag:{display:{Name:"Rupee"}}}]}

does not.

I am trying to make a Zelda like shop system - so the player score of an objective called "Rupees" has to be exactly the same as the amount of items called Rupee the player has in his inventory (because /clear does not have a minimum value).

It works with the values 1-50 (max moneybag size, because 50 command-blocks is much) but not with zero.

So if a player buys an item and I remove the rupees, the scoreboard will never be zero even if the player has no more rupees - and therefore he can always keep buying items.