Rabada trapped Smith leg before wicket on the opening day of the second test at St George's Park on Friday and appeared to brush against the batsman in his celebration as the Australian walked down the pitch.
The hearing will be heard by match referee Jeff Crowe on Saturday evening, with Rabada set to contest the charge. The bowler already has five demerit points and three more would earn him two suspension points that would result in a two-test ban and rule him out for the rest of the four-match series.
Captains meet to curb bad blood ahead of second Test
Rabada picked up three demerit points 12 months ago when he was adjudged to have led with the shoulder into Sri Lankan Niroshan Dickwella in a One-Day International, before picking up one demerit point each for swearing at England's Ben Stokes and Indian opener Shikhar Dhawan, the latest offence just last month.
Demerit points remain on a players' record for a period of two years. If Rabada is found guilty of the Level Two offence, it carries a minimum sanction of three points.
He would be the third player to receive punishment in the tempestuous test series so far, with David Warner (three points) and Quinton de Kock (one) each sanctioned for a verbal spat at tea on the fourth day of the first test.
Australian spinner Nathan Lyon (one) was found guilty of deliberately dropping the ball on a sprawled AB de Villiers after the latter was run out in the same game.
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