The 19-foot statue, covered entirely in gold leaf, honours the Alabay or Central Asian shepherd breed.
Many of the infection-free countries closed their borders to all foreign travelers from the early stages of the pandemic.
"The Turkmen authorities have lived up to their reputation by adopting this extreme method for eradicating all information about the coronavirus," Reporters Without Borders' Jeanne Cavelier said.
Just over 20 countries have yet to record a single COVID-19 coronavirus case, most in the relatively lightly-afflicted continent of Africa and isolated Pacific island states, but also others much closer to major outbreaks.
Turkmenistan Airlines was popular among Sikhs flying to the Indian city of Amritsar.
Could Russia benefit from U.S. attention waning or will China step in?
After changes to the constitution in 2016 Berdymukhamedov could rule indefinitely.
There is no longer a legal barrier on Kurbanguly Berdymukhamedov's potential re-election.
Berdimuhamedov has been following the March 8 tradition since 2013.