The move follows Rome's decision not to bid for the 2024 Olympics and it leaves Ireland, France and South Africa in the running to stage the tournament.
"Our candidature was strictly connected to the Olympic bid," said Italian Rugby Federation president Alfredo Gavazzi.
"As agreed with the government and Olympic committee, we can't provide necessary commitments to move forward."
He added: "We remain convinced of the strength of our bid and are well aware of the benefits that hosting the Rugby World Cup would have brought to Italy.
"We're conscious about losing a fantastic chance to promote our values and our sport in our country, but we must sadly accept that we can no longer move forward with our bid."
Ireland formally announced their bid in December 2014 and a final decision on the hosts will be made in November next year.
As well as the traditional rugby stadiums such as the Aviva in Dublin, the Kingspan at Ravenhill in Belfast and Thomond Park in Limerick, a 2023 World Cup in Ireland would also hope to utilise a number of impressive Gaelic football venues, including the 82,300-capacity Croke Park in Dublin.
Ireland's hopes of hosting the 2023 Rugby World Cup have been boosted after Italy withdrew their bid on Wednesday.