Bigi, who had yet to make an appearance in France where Italy have defeated Namibia and Uruguay, has been ruled out due to a second-degree muscle injury to the adductor of his right leg.
Manfredi, 26, plays his club rugby with Zebre Parma. He has made two appearances for Italy, both coming off the bench and both at Murrayfield against Scotland.
He was selected in Italy's 2023 Six Nations squad and made his debut in the final game as the Azzurri lost 26-14 to Scotland. He was included in Kieran Crowley's 46-man preliminary squad for the World Cup and played in the 25-13 loss to Scotland in the Summer Series in July.
Manfredi didn't make the cut when coach Crowley named his final 33-man squad for the World Cup, but will now join the group in France on Sunday as they prepare for the pool A game against New Zealand on Friday.