Wilson was born in Dhahran, Saudi Arabia where his father, Jim Wilson, worked as a geologist for Aramco. Jim played college football in the NAIA at Hanover College before being cut by the Cincinnati Bengals, declining an offer from the Green Bay Packers and returning to graduate school.
The family moved to New Orleans when Wilson was two years old and then moved to Kingsport, Tennessee, where Wilson spent the majority of his youth. Wilson grew up as a Boston Red Sox fan.
Wilson attended Hurricane High School in Hurricane, West Virginia, then attended Winthrop University. Collegiate Baseball named him the National Freshman Pitcher of the Year in 2006. In the summer of 2007, he had Tommy John surgery. He transferred to Texas A&M University in January 2008. He was drafted by the Chicago Cubs in the 10th Round of the 2008 Major League Baseball Draft, but did not sign. He was drafted by the Boston Red Sox in the 2nd Round of the 2009 Major League Baseball Draft. In November 2012, Wilson was added to the 40-man roster to protect him from the Rule 5 Draft.
On March 16, 2013, Wilson was optioned to the Triple-A Pawtucket Red Sox to begin the season. He was called up to the Red Sox on April 7 when John Lackey went on the disabled list, and made his Major League debut on April 11. He was optioned to Pawtucket on May 29, and recalled on June 13 when Alfredo Aceves was optioned to Pawtucket.
Wilson pitched in the Major Leagues for parts of the 2013 and 2014 seasons. He threw 27 2⁄3 innings for the Red Sox in 2013 and posted a 4.88 ERA. He performed much better in his 28 1⁄3 Major League innings in 2014, recording a 1.91 ERA.
On December 11, 2014, the Red Sox traded Wilson along with Gabe Speier and Yoenis Céspedes to the Detroit Tigers for Rick Porcello.
On May 27, 2015, Alex Wilson got his first career major league start for the Detroit Tigers against the Oakland Athletics, where he went 3 scoreless inning with 52 pitches. Detroit went on to win 3–2.
On July 30, 2015, Wilson earned his first major league save, getting the final five outs in a 9–8 Tigers win over the Baltimore Orioles. For the season, he pitched 70 innings (including a team-high 67 in relief), with 16 games finished, 2 saves, a 2.19 ERA and a 1.03 WHIP.
During the 2016 season, Wilson set career highs with 62 appearances and 73 innings, while posting a 4–0 record with a 2.96 ERA, with 49 strikeouts and 21 walks.
On January 13, 2017, the Tigers avoided arbitration with Wilson, agreeing on a one-year, $1.175 million contract. On August 25, Wilson was ejected for the first time in his Major League career after hitting Todd Frazier with a pitch. This followed after Miguel Cabrera and Austin Romine were ejected for triggering a bench-clearing brawl and after Dellin Betances was also ejected for the first time in his Major League career after hitting James McCann with a pitch. The next day, on August 25, Wilson was suspended for four games. He began serving his suspension on September 2 after it was reduced to three games following an appeal.
On September 23, Wilson sustained a non-displaced fractured right fibula after he was hit by a line drive off the bat of Joe Mauer, ending his season. During the 2017 season, Wilson posted a 2–5 record, 4.35 ERA, and 42 strikeouts in 60 innings pitched.
Wilson throws three primary pitches. He has a four-seam fastball that averages 92 mph (tops out at 96 mph), a two-seam fastball at 91-92 mph (tops out at 95 mph), and a slider in the 86-88 mph range (tops out at 90 mph). Wilson himself has described his two-seam fastball as a cutter, though PitchFX lists it as a two-seamer. He also throws an occasional curveball and changeup.
Wilson played high school baseball at Hurricane High School where he won a state championship in 2002.
Wilson is the second Saudi-born player in MLB history, after Craig Stansberry.