The government has faced growing criticism of its handling of the outbreak.
Some opposition politicians have been particularly critical of the health minister who they not only want to be sacked, but jailed.
Opposition politicians from the Party of the Regions say the first reported cases were at the beginning of October, but by middle of the month there had already been confirmed deaths.
They say the authorities should have provided accurate information about the outbreak so that Ukrainians could seek appropriate medical help.
Instead, the opposition says, many people have resorted to self-treatment.
Experts say Ukraine was unprepared for the swine flu outbreak, and the hunt for political scapegoats is likely to continue.
The opposition leader, Viktor Yanukovych, has called on parliament to scrutinise the government's actions.