WASHINGTON — The Giants, who have had rotten luck with broken hands the past few seasons, took another blow Tuesday when top prospect Joey Bart was diagnosed with a fracture in his left hand.

Bart was injured Monday night when hit by a pitch from Stockton’s Mitchell Jordan in San Jose in a Class A game. Diagnostic tests and doctors confirmed the fracture in the second metacarpal.

Giants manager Bruce Bochy said Bart’s hand was placed in a cast and will be re-evaluated in about two weeks, although the catcher likely will miss 4-6 weeks.

Bochy called this a “minor setback” for last year’s No. 2 overall draft pick, who was expected to have a quick rise through the Giants’ minor-league system before reaching the majors.

The 22-year-old had a good spring training with the Giants, hitting .350 with a homer and two doubles, and was 10-for-37 (.270) with two home runs for San Jose when Jordan, an A’s prospect, hit him in the fourth inning of Stockton’s 6-1 victory.

“You just hate to see it for the kid because he had a great spring and was getting off to a great start, and now he’s going to miss some time,” Bochy said.

President of baseball operations Farhan Zaidi had said a September call-up for Bart was not out of the question. The injury will make that tougher with Bart not expected to return to San Jose before June, but not impossible.

“There’s a lot of baseball left,” Bochy said.

Bochy reflects: Washington is the first city Bochy will visit for the final time on his farewell tour and carries much nostalgia. He spent part of his youth living in nearby Falls Church, Va., where the team is staying, played youth baseball in D.C. and saw his first big-league game at RFK Stadium when he was 11.

“This is kind of where it started for me as far as really having a passion and desire to play baseball,” Bochy said. “Driving to the ballpark, I did think about it.”

Several friends who played youth baseball with Bochy planned to attend Tuesday night’s game and spend time with the manager afterward.

Briefly: Bochy said he hopes Tyler Austin’s inflamed right elbow is healthy enough to allow him to start in left field against lefty Patrick Corbin in Thursday’s series finale. … The Giants’ bullpen threw 20 shutout innings in four games against Colorado, the second most in any series in the past 100 years. Houston relievers threw 25 in a 1989 series against the Dodgers.

Henry Schulman is a San Francisco Chronicle staff writer.