(Bamidbar 31:24) "And you shall wash your garments on the seventh day and you shall be clean": What is the intent of this? Since we are speaking of one slain by the sword, Scripture comes to teach us that the sword and one who touches it is tamei for seven days. Whence do we derive (the same for transfer of tumah from) vessels (i.e., appurtenances) to man to vessels (appurtenances)? From "And you shall wash your garments." "and then you shall come to the camp." Just as here, (without washing of garments and sprinkling) he is forbidden to enter the camp (of the Shechinah), so, there (vis-à-vis the red heifer, Vayikra 19:19) he is forbidden to enter the camp; and just as there, until the evening, so, here, until the evening.
Laws of Purification After Contact with Death
Sifrei Bamidbar 158:3