General manager Steve Kerr made the announcement before Saturday night's game against Golden State.
Barbosa had the cyst drained in November but it returned and had been increasingly bothering him for the past two weeks.
Kerr says the surgery will be performed as soon as possible, probably on Monday.
Barbosa missed three games with the wrist problem, then sat out 12 games in December with an ankle injury.
Jason Richardson will move back into the starting lineup in Barbosa's absence. Coach Alvin Gentry had moved Barbosa and Robin Lopez into the starting lineup three games ago in place of Richardson and Channing Frye.
Barbosa, the NBA's sixth man of the year in 2006-07, is averaging 10.7 points per game.
Known for his energy and shooting ability, Barbosa had struggled from the field, going 12 for 32 in the last three games, 4 for 17 from 3-point range.
Pain and swelling in the wrist contributed to the shooting problems, Kerr said.
"The biggest thing is he's been trying to shoot through it and you can see it's really, really swollen," Kerr said, "so he hasn't had the flexibility in his wrist to be able to get the ball in the right position."
Kerr said Barbosa should be able to start running and doing other conditioning work a week after the operation, which should speed up his return once he's cleared for basketball activity.