The National Prosecuting Authority head Shaun Abrahams asked South Africans to "stop deriving political mileage of this matter," following media reports last week that the minister's arrest was imminent.
Earlier the Hawks police unit said it has no plans to arrest Gordhan.
Gordhan, who was reinstated as finance minister in December, had said last week that a newspaper report of his imminent arrest was an attack on the Treasury.
"He is not a suspect," Hawks spokesman Hangwani Mulaudzi told Reuters, adding that the unit was not singling out Gordhan in its investigation of the surveillance unit.
The Hawks is investigating a surveillance unit within the South African Revenue Service (SARS), Mulaudzi said. Gordhan headed the SARS between 1999 to 2009.
The Sunday Independent reported at the weekend that Hawks chief Berning Ntlemeza had sent Gordhan's lawyers a letter to reassure him he would not be arrested.