"The Post Office heads of human resources as well as security and investigations have been placed on precautionary suspension while the investigation is proceeding," her spokesperson Nthabeleng Mokitimi-Dlamini said.
The Sunday Times reported earlier this month that Mrwetyana's confessed killer was on a list of 300 Post Office employees flagged by the State Security Agency in June 2018.
Despite being aware that he had a criminal conviction, no action was taken.
"The Post Office is in the process of further investigations to ascertain the appropriate actions to be taken against identified employees. In this respect, the minister urged the Post Office to swiftly act on affected employees, especially those in the mail and frontline services," Mokitimi-Dlamini said.
Ndabeni-Abrahams has also instructed her director-general to ensure there is security vetting at all state-owned entities that fall under her department.