The Ministry of Public Enterprises has condemned what it calls "reckless and insensitive tweets and reports" questioning Minister Pravin Gordhan’s health.
On Sunday, the ministry said the reports were "fake news" that was "meant to distract and cause unnecessary confusion in the market".
"I’m well and working hard for the country. This is clearly mischief created by the corrupt and desperate elements in South Africa who wish to go on stealing, neglect the poor and abuse public resources," Gordhan said in a statement.
The ministry said Gorhan "continues to be engaged in matters of the state to ensure that our state-owned enterprises are stabilised and play a critical role in the economic recovery of the country".
The ministry did not say which tweets and reports it was responding to.
Earlier in the day former top Eskom executive Matshela Koko tweeted "is he okay?" in reference to Gordhan. His tweet was retweeted over 100 times and liked more than 400 times.