According to Comair, its planes were grounded after a notice was issued relating to irregularities found during an audit of its maintenance and technical service provider.
The airline said it has contingency plans in place and aims to minimise any disruption to its operations.
Kulula and British Airways customers are urged to check their flight status on the websites, ba.com and kulula.com.
“We do apologise to our customers for any inconvenience to their travel plans and appreciate their support.
“We are working closely with Saat (SA Airways Technical) to rectify the findings and get our flights back on schedule as soon as possible,” Comair said.
SAA also warned customers of possible disruptions, after the aviation authority recalled some aircraft to undertake compliance verification.