Because of the modifier: "de spălat" ("for washing"), which indicates the type of machine we're speaking of.

If the sentence was "Ea pune prosopul în mașină" that would most likely mean "She puts the towel in the car."

Because you refer to that "washing machine" not in general to a "washing machine"

Like if you say "Come and buy a washig machine from us" then you could say "Vino și cumpără o mașină de spălat".

That because you don't talk about your washing machine or other one. You talk about it in general.