The solution is to pass the function as a lambda:
from Tkinter import *
root =Tk()
def callback(parameter):
print parameter
button = Button(root, text="Button", command=lambda: callback(1))
button.pack()
root.mainloop()
Also, as @nbro already correctly pointed out, the button attribute is command, not function.
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solved Tkinter Function attached to Button executed immediately [duplicate]