The scheme invited offers for about 11.7-million MTN shares.
Small investors who signed-up for the R2000 minimum purchase will get their full allocation of about 25 MTN shares, but people who offered for the maximum R50 000 worth of shares will probably be limited to an investment of R46000, the fund's spokesman, Moemise Motsepe, said.
Institutions that signed-up for the R100000 maximum will also probably get their allocations cut back.
The extent to which the Asonge offer has been over-subscribed is not yet known because the applications received by Friday's deadline are still being tallied.
The final allocation of shares will depend on MTN's closing price on August 30. But it is clear that more black South Africans have signed up for the Asonge deal than can be accommodated, Motsepe said.
Under the Asonge deal, black investors are able to buy MTN shares for R79.61 each ? a 20percent discount to MTN's R99.51 closing price when the offer opened on July 23.
The final price might be even lower if MTN shares are below R99.51 when the JSE closes at the end of this month.
The cellphone network operator's stock crashed, along with most others on the JSE last week, but looked as if it were well on its way to making a recovery by yesterday.
The government made the MTN shares available to blacks through the Post Office.