MSC, led by Gianluigi Aponte, had initially seen an investment as a way of expanding beyond its cruise and container shipping business.
In a short statement, MSC said it did not now see the right conditions for a deal in the current process.
The privatisation is proving a headache for the Italian Treasury.
It reopened the process at the end of last month after an exclusivity period for talks with US private equity fund Certares, Air France-KLM and Delta failed to produce a deal.
Lufthansa Still Interested
A Lufthansa spokesman said last week that it was still interested in buying into ITA despite reports that MSC had pulled out.