The virus has since been detected in Belgium, Botswana, Israel and Hong Kong.
The South African foreign ministry has now released a strongly worded statement criticising the travel bans.
"This latest round of travel bans is akin to punishing South Africa for its advanced genomic sequencing and the ability to detect new variants quicker," the Ministry of International Relations and Cooperation said.
"Excellent science should be applauded and not punished," it said in a statement.
The foreign ministry noted that while the new variant was also detected in other countries, the global reaction to those countries have been "starkly different" to cases in southern Africa.
The new variant was first announced on Wednesday by a team of scientists in South Africa who said they had detected a variant that could possibly evade the body’s immune response and make it more transmissible.
On Friday the World Health Organization named it Omicron and designated it as a "variant of concern" - its most serious level - saying preliminary evidence suggests an increased risk of re-infection.
"Our immediate concern is the damage that these restrictions are causing to families, the travel and tourism industries and business," South African Foreign Minister Naledi Pandor said in the statement.
The government was engaging with countries that have imposed travel bans to persuade them to reconsider, it added.
On Friday, the WHO cautioned countries against hastily imposing travel restrictions linked to the variant, saying they should take a "risk-based and scientific approach".