The Congress of the People laid fraud charges against her for misrepresenting her educational qualifications in 2015.
"The docket was handed over to the National Prosecuting Authority for a decision. The decision has now been made for her prosecution.
Sowetan has learnt that the warrant for Tshabalala's arrest was issued after police searched for her for months without success at her Bryanston, Johannesburg, home.
But Tshabalala, when contacted for comment yesterday, said she was not in hiding.
"I honestly have no idea what you are talking about. I have not disappeared.
"I'm in South Africa, I just hope they leave me alone and I have no reason to leave [the country] for anything."
The house which she provided as her residential address had apparently been deserted for a while, with neighbours indicating they've not seen her in months.
Tshabalala, a close ally of former president Jacob Zuma, allegedly lied about her academic qualifications when applying for the job of the public broadcaster's chairperson.
Her CV had stated she had obtained a BCom degree and a postgraduate degree in labour relations from University of South Africa (Unisa). However, Unisa stated that, according to its records, she had neither of these qualifications.
In August, a commission of inquiry into interference at the public broadcaster found that from 2012 to 2017, SABC executives took instructions from "people with no authority in the newsroom".
The report specifically cited Tshabalala among those fingered in this regard.