Stavos Kontonis ordered an inquiry after "denunciations concerning bribes paid to functionaries by Novartis" appeared in the press, a ministerial statement said.
"The judicial investigation will be swift and thorough," it added.
According to a judicial source, a preliminary investigation has been going on for two months and around 178 people in Greece have been questioned.
The source said anti-corruption prosecutors had visited Novartis's premises near Athens to gather evidence.
The case gained attention in recent days following a suicide attempt in Athens on Sunday, New Year's Day, by a Novartis manager.
That attempt was thwarted by police and according to the judicial source, the manager was one of those questioned over corruption.
For its part Novartis issued a statement saying it was "aware of the media reports about our business practices" in Greece and that it was seeking more information and was cooperating with the authorities.
"Novartis is committed to the highest standards of ethical business conduct and regulatory compliance in all aspects of its work and takes any allegation of misconduct extremely seriously," the company said in the statement.
The judicial source also claimed American FBI agents were in Athens to help Greek authorities investigate Novartis.
The Swiss pharmaceutical giant was investigated by US authorities in 2014, accused of paying bribes in order to boost sales of some of its medicines, and was later fined $390 million by the US Justice Department.