Mexico City had been due to host the second round of season seven on Feb. 13 while the Chinese resort of Sanya was scheduled for March 13.
This year's Chinese Formula E round was the first major motorsport event to be cancelled due to the pandemic.
The 2019-20 Formula E season ended in August with six races in Berlin after a spate of cancellations.
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"In all decision-making we prioritise the health and safety of our staff and the entire Formula E community... as well as the citizens and residents of the cities in which we race," Formula E said in a statement.
It said the Chilean capital Santiago would host two season-opening races on Jan. 16 and 17 but without spectators.
Diriyah, in Saudi Arabia, will then host a double-header of races on Feb. 26-27, with planning for spectators to be allowed on site.
The series, which is now an FIA-recognised championship, said it will confirm subsequent races in early 2021. (Reporting by Alan Baldwin, editing by Christian Radnedge)
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