Authorities in the southern Ba Ria-Vung Tau Province, home to the island, had sought the suspension saying Con Dao has difficulty implementing Covid-prevention measures because of its distance from the mainland, and it could be very dangerous if the outbreak spreads to it.
But helicopter flights from Vung Tau to Con Dao are still allowed for carrying medical supplies.
On Friday provincial authorities also announced plans to test all 10,000 residents on the island for coronavirus by Sunday, and are planning to vaccinate all of them.
Ba Ria-Vung Tau, which neighbors HCMC, now a coronavirus hotspot, has closed its public beaches and suspended boat services to Con Dao since Tuesday.
Authorities in Phu Quoc, Vietnam's largest island, have also called for suspending all flights and not allowing visitors from Covid-hit places to board ferries in nearby towns like Ha Tien and Rach Gia.
Phu Quoc, which has a population of 102,000, has become a top tourist destination after the government rolled out a 30-day visa-free policy for foreigners in 2014.
The island received over five million visitors in 2019, including 541,600 foreigners.
HCMC has been grappling with a surge in community transmissions over the past week, mainly linked to a cluster at Christian congregation Revival Ekklesia Mission.
The city of 13 million began two weeks of social distancing on Monday.
It has so far recorded 324 infections during the fourth wave.
Many provinces have stopped public transport to and from HCMC and require people arriving from the city to quarantine for 21 days.