Enoch Godongwana has been accused of having inappropriately touched a masseuse at a luxury wildlife lodge earlier this month.
He denies the allegations, saying his wife was in the same room when he received the massage.
The incident allegedly took place at a hotel in the renowned Kruger National Park on August 9, when Godongwana is alleged to have assaulted a member of staff who provided in-room massage services.
It has piled pressure on the ruling African National Congress ahead of a key conference in December, when the party is to pick a candidate for the next presidential election.
South Africa's National Prosecuting Authority (NPA) said it was expecting to receive the case docket from police on Monday.
"The prosecution needs time to study the docket... (and) see the evidence that they have," NPA spokeswoman Monica Nyuswa told AFP, adding it might take weeks before a decision on whether to prosecute is taken.
Godongwana has suggested he would resign if charges were pressed against him.
"I, in no way or at any time inappropriately touched, sexually harassed, or assaulted anyone," the minister said in a statement last week.
"I take the allegations very seriously. As such, I am looking forward to the necessary legal processes unfolding."
Godongwana was appointed to lead the finance ministry by President Cyril Ramaphosa last year.