The decision confirms what three sources had told Reuters on Friday. The trial was originally expected to start on Monday.
The case involves the 2011 purchase by Eni and Shell of Nigeria of Nigeria’s OPL-245 offshore oilfield - one of Africa’s most valuable oil blocks - for about $1.3 billion (941.07 million pounds).
Milan prosecutors allege bribes were paid to win the license to explore the field, which has never entered into production.
All the accused have denied any wrongdoing.
A Milan judge ruled in December that the companies, along with present and past executives, would face trial.
Reporting by Manuela D'Alessandro; writing by Francesca Landini; editing by Agnieszka Flak