Lawmakers from the ruling coalition said a special parliamentary commission was not competent to examine the case and sent it back to the courts, state news agency ANA said.
Protected witnesses have said that nearly a dozen senior politicians, including former prime minister Antonis Samaras, Greek central banker Yannis Stournaras and EU migration commissioner Dimitris Avramopoulos, were allegedly involved in helping Novartis build a commanding position in the Greek health market.
The Swiss giant is suspected of having bribed decision-makers and doctors between 2006 and 2015 to secure inflated prices for its products even though cheaper alternatives were available.
The scheme is estimated to have cost the Greek state some three billion euros ($3.5 billion).
The bribes were usually hidden in overpriced company invoices for medical congresses and trips, but money is suspected to have also occasionally been given directly, witnesses said.
All those named deny wrongdoing, and some have sued the witnesses for perjury and defamation.
Novartis has said it is cooperating with Greek authorities whilst conducting an internal audit of its own. The Swiss giant has already paid multi-million dollar fines in the United States, China and South Korea to settle corruption cases.