The required recovery time will be known on Monday but Neto is unlikely to be fit for Barca's opening La Liga game away to Athletic Bilbao on Friday.
"In the last training session, first team player Neto suffered a bruise on his left wrist," a club statement read.
"The tests have diagnosed a scaphoid bone fracture. The treatment is to follow and the time the player is out for will be determined on Monday."
Neto joined Barcelona this summer from Valencia, with fellow goalkeeper Jasper Cillessen leaving Camp Nou and going the other way.
Coach Ernesto Valverde is already likely to be without Lionel Messi against Bilbao. Messi missed the friendly win over Napoli on Saturday after sustaining a calf tear in training last week.