The influential National Security and Defence Council has called on the judiciary to investigate why Ukraine was unable to prevent the outbreak.
President Viktor Yushchenko has even asked the country's security service to look at whether pharmacies are guilty of price-fixing anti-flu medications.
Critics have also rounded on Ukrainian television channels which they say have wall-to-wall coverage of Ukraine's leading politicians, but not leading medical specialists.
This, they say, is exacerbating public concern rather than allaying popular fears.
Some analysts say swine flu is being used by the President and his arch rival the Prime Minister Yulia Tymoshenko to score political points ahead of presidential elections in January.
Supporters of Prime Minister Tymoshenko, who remains at bitter loggerheads with the President, say he is trying to blame her government for the situation.