The rand slid against the dollar on Wednesday morning on fears that Gordhan will be arrested..
On Thursday night, the Johannesburg Magistrate's Court dismissed an application by the trade union federation for authorisation on the highway motorcade.
Congress of SA Trade Unions spokesman Patrick Craven said the protest would go ahead, despite the ruling.
"We will be going ahead with the protest...We urge all people to assemble at Cosatu house tomorrow [Friday] at 8am."
The union federation approached the court after failing to get permission from the Johannesburg metro police.
Metro police chief Superintendent Wayne Minnaar said authorisation was not granted because at Cosatu's previous motorcade, protesters had stopped and walked along freeways, which was in contravention of the National Road Traffic Act.
Minnaar said all law enforcement agencies would be on standby on Friday to ensure the protest did not go ahead.
Earlier this week, Cosatu's Gauteng secretary Dumisani Dakile said the planned motorcade was to be held on the M1 north, N1 south, N12, and M2 north highways in Johannesburg.
In December, the N3 highway was briefly closed when protesting motorists parked their cars sideways and started dancing on the road during a similar drive-slow motorcade.
Electronic tolling is due to be implemented soon.
On April 11, the SA National Roads Agency Limited announced it would be rolled out within the next two months.
In April last year, the High Court in Pretoria granted the Opposition to Urban Tolling Alliance (Outa) an interdict approving a full judicial review before e-tolling could be put into effect.
The interdict prevented Sanral from levying or collecting e-tolls pending the outcome of the review. Sanral and the National Treasury appealed the court order.
In September, the Constitutional Court set aside the interim order, and in December the High Court in Pretoria dismissed Outa's application to scrap e-tolling.
On January 25, the court granted Outa leave to take the matter to the Supreme Court of Appeal (SCA) in Bloemfontein.
The SCA hearing will take place in September.