Mr Putin claimed on Tuesday that one of his adult daughters had already been inoculated with the vaccine, which he insisted had passed necessary tests and been proved to be effective.
However, scientists from outside Russia have warned there is so far no published scientific evidence to support the claims.
Professor Francois Balloux, director of University College London’s Genetics Institute, said the decision to approve the vaccine so quickly was “reckless and foolish”.
“Mass vaccination with an improperly tested vaccine is unethical,” Professor Balloux said.
“Any problem with the Russian vaccination campaign would be disastrous both through its negative effects on health, but also because it would further set back the acceptance of vaccines in the population.”
The approval of the vaccine by Russia’s health ministry has come before the start of a larger Phase III trial involving thousands of participants.
Such trials, which require a certain rate of participants catching the virus to observe the vaccine's effect, are normally considered essential precursors for a vaccine to receive regulatory approval.
Eleanor Riley, a professor of immunology and infectious disease at the University of Edinburgh, noted that there were precedents for rapid approval of vaccines in epidemics but usually in high risks situations, such as the Ebola outbreak in West Africa.
“Arguably, these justifications do not (or no longer) pertain in the case of the Covid-19 pandemic,” Professor Riley said.
“The individual risk of dying from Covid-19 is low, and in many countries it is falling, and we have effective public health measures to sustain this in the short to medium term.”
Due to the low rate of infections in Europe, some research teams have set up vaccine trials in Brazil and the US where cases are much higher to test their effectiveness.
The World Health Organisation (WHO) said it had set up discussions with Russian health authorities to work on a process for possible prequalification for the country’s vaccine.
“We are in close contact with Russian health authorities and discussions are ongoing with respect to possible WHO prequalification of the vaccine, but again prequalification of any vaccine includes the rigorous review and assessment of all required safety and efficacy data,” Tarik Jasarevic, a WHO spokesperson, told a UN briefing in Geneva.
Mike Turner, head of major science investments at the research charity Wellcome, warned that safety was “the most important consideration” for vaccine development.
“Covid-19 is the greatest vaccine development challenge in history, but speed should not compromise safety,” Mr Turner said.
“Without the data on this vaccine being released, it is impossible to assess its efficacy or safety – even in early testing – but this data must be shared openly and transparently to maintain public trust.”
He added that all vaccines must go through “robust clinical trials”, including Phase III trials, to ensure safety and test for any potential rare side effects.
“To bring this pandemic to an end we need safe and effective vaccines, treatments and diagnostics for Covid-19 available to everyone, everywhere.”
Additional reporting by agencies