At 0730 GMT, the rand traded at 14.3950 versus the dollar, barely changed from its previous close.
The rand had tumbled on Thursday, as investor fears that the coronavirus could spread boosted safe-haven currencies and dented demand for riskier emerging market units.
South Africa's Department of Health said on Thursday that port health authorities had enhanced surveillance for all travellers from Asia.
A weak growth outlook for the South African economy has sapped demand for rand assets, after the International Monetary Fund and South African Reserve Bank downgraded their growth predictions.
Government bonds dipped in early deals on Friday, with the yield on the 2026, instrument rising 2 basis points to 8.155pc.
The blue-chip Top 40 index on the Johannesburg Stock Exchange was 0.6pc stronger.