The 30-year-old Brazilian picked up the injury in training prior to the friendly game against Napoli at the weekend, which the Catalans won 4-0.
Neto only joined Barcelona from Valencia in the off-season for £23m with Netherlands international goalkeeper Jasper Cillessen departing the Spanish champions in the opposite direction.
"Doctor Xavier Mir successfully carried out surgery this morning on a fractured scaphoid bone on the left hand of first team player Neto. The down time will be around six to eight weeks," a club statement read.
Neto’s injury has left Barcelona manager Ernesto Valverde without an accomplished deputy for first choice goalkeeper Marc Andre ter Stegen, and Inaki Pena will be called from the club’s reserve side to serve as cover for the German.
Barcelona will therefore be without Neto for their La Liga opener against Athletic Bilbao on Friday.
The timescale for his recovery means Neto is not expected to feature for Barcelona until after the international break in October.
Another player who might be absent for Friday’s La Liga opener is captain Lionel Messi, who missed the game against Napoli due to a calf injury sustained in training last week.
"He's in the recovery process and I don't know if he will be ready for the start of La Liga," Valverde told a news conference after the 4-0 win over Napoli in Michigan on Saturday. "It's looking difficult."
