The 21-year-old American, who won the NBA 3-Point Contest at last season's All-Star Weekend, sprained his right hand in March and missed the Suns' final 12 games.
Booker averaged 24.9 points, 4.7 assists and 4.5 rebounds a game last season for the Suns, who have not reached the playoffs since 2010. They went a league-worst 21-61 last season, their fourth consecutive losing campaign.
Booker posted an image of himself on Instagram with a cast on his hand and the message: "Thank you for all the prayers and well wishes. First surgery was a success. Lefty buckets coming soon."
The procedure, performed by Dr. Steven Shin in Los Angeles, repaired the fifth metacarpophalangeal joint in his right hand and was expected to sideline Booker for six weeks.
That would cause him to miss the entire pre-season and the first week of the 2018-19 campaign. The Suns open at home against Dallas on October 17 before visiting Denver and reigning NBA champion Golden State on October 20 and 22 respectively.
Booker, the 13th overall pick in the 2015 NBA Draft, signed a five-year maximum extension worth $158 million in July after the best of his three NBA seasons, all with Phoenix.