Translation:They will have brought the medicine by tomorrow.
Because the perfect tense refers to the completion of an action, not to a duration.
A completion does not take a long time, but "until" refers to an action that lasts a long time (and ends at a specific time).
"by tomorrow" means that the action takes place somewhere between now and tomorrow, but "until tomorrow" means that the action takes place all the time (continuously) from now and ending tomorrow.
What? If anything, it should be the other way around. "Medicine" may refer to the entire discipline or field, but "medication" always refers to a physical substance, a pharmacological preparation.
Edited to add: Ooops! Apparently αγωγή can mean "treatment", and obviously does here. Nothing to do with education or learning. However, I do stand by "medication" being a valid translation here - in most contexts, "medication" and "medicine" are synonymous.