White Sox promoted Kenny Williams to Executive Vice President; Rick Hahn became the team's new General Manager.
The Sox went to Toronto where they faced the top favorite in the AL East, the Blue Jays.
That was the seventh consecutive seasons that they played four-game series in Toronto, and the Sox are 9–19 in that span.
The team went straight to Kansas City, but the opening game was postponed due to rain.
Before the game, it was announced that Gavin Floyd would undergo Tommy John surgery and miss 14–19 months.
In the series finale, which was a make-up game from three days earlier, Alexei Ramírez hit a long ball that was ruled foul but video showed it was actually a home-run that would have given the Sox the lead.
In the eleventh inning, Jordan Danks hit the solo shot for a 2-1 Sox lead and went on to win by that score.
In the first of two-game set against them, the Sox went almost offenseless as only one batter reached base via an infield single by Alex Ríos in the seventh.
Mets ace Matt Harvey shut down the Sox lineup for nine innings, striking out a career-high twelve batters.
After the series win, the Sox played three against the Marlins, who at the time had the worst record in baseball.
The Sox then played consecutive home-and-home series against the crosstown rival Cubs, starting with two in the South Side and finishing with two at Wrigley Field.
In the third game of that series on June 5, neither team scored runs until the 14th inning when Sox scored five runs in the top half, but the Mariners tied it in the bottom half with a grand slam by Kyle Seager.
Jesse Crain gave up runs (all unearned) for the first time since April 12, snapping the franchise record 29 straight scoreless appearances.
In the first game, Addison Reed blew his save in the ninth when Daniel Murphy hit a popup, Gordon Beckham ran towards the territory where Reed and Conor Gillaspie were calling for but Beckham got in the way and no one caught the ball.
However, in the bottom of the ninth inning Alexei Ramírez hit a walk-off single, scoring Jeff Keppinger for a 5–4 Sox win.
In Game 2, the Sox led 8–5 going to the ninth inning but Reed blew his second straight save by allowing four runs including game-winning solo home run by former Sox Nick Swisher and went on to lose 9–8.
After that series win, they headed to St. Pete where they get swept by Rays scoring only 4 runs during the three-game sweep.
The last White Sox player to have six hits in a 9-inning game was Lance Johnson on September 23, 1995, against the Twins.
Just before the series began, Matt Thornton and cash was traded to the Boston Red Sox for minor leaguer Brandon Jacobs.
Before the series against Cleveland, the Sox traded Jesse Crain to the Tampa Bay Rays for players to be named later and/or cash considerations.
In game one, the Sox lost 3-2 due to a pinch-hit walk-off homer by 42-year-old veteran Jason Giambi.
Before the first game of the series, it was announced that Yankees third baseman Alex Rodriguez was given a 211-game suspension for his part in the Biogenesis baseball scandal.
Before the doubleheader, Alex Ríos was claimed off waivers by the Rangers for Leury García.
In that game, pitcher Jake Petricka made his MLB debut and also got his first major league victory and Conor Gillaspie hit the game-winning home run in the top of 12th.
The last time a pitcher got a save in six straight games was in 2003 when Éric Gagné of the Los Angeles Dodgers accomplished the feat.
According to Elias Sports Bureau, it was the first time since June 5, 1955, that a player homered in support of his brother on the mound, when Kansas City Athletics catcher Billy Shantz homered for his brother Bobby Shantz.
The Sox finished the month on a 10-game road trip on the east coast starting with three in Boston.
The Sox would then get swept in a four-game series at home against the Indians for the second time this season and third overall.
It was the first time in franchise history that Sox had a lead by six or more runs in the ninth inning or later and lost.
The Sox won that game 3–2, backed by the first major league home run by Marcus Semien.