"He is not happy. That's why he is instructing [to apply for leave to appeal]," defence lawyer Bantubonke Tokota told reporters after the court adjourned.
"We have been instructed to appeal against both the conviction and sentence."
Asked whether Motata was concerned about reports that his job might be under question, Tokota said: "We are all concerned.
"What is in drunken driving? There is nothing impeachable in it as far as we are concerned."
Prosecutor Zaais van Zyl said Motata had a right to appeal.
"We will be opposing it."
The date of the application is expected to be decided early next week.
Motata was on Wednesday sentenced to a R20 000 fine or 12 months' imprisonment for drunken driving.
A video of a boy being forced by his parents to run almost naked in the snow has sparked an uproar.
Cosatu met with the Public Protector to discuss its numerous complaints against Premier Helen Zille.
Marine ruins have been discovered by builders working at the V&A Waterfront in Cape Town.
