In baseball, Szczur served as an outfielder and catcher for the Wildcats. After sitting out his freshman year due to a football-related injury, Szczur hit.392 with 62 RBI and 28 stolen bases over the next two seasons. During his junior season, he was a First Team All-Big East selection and named the Philadelphia Big 5player of the year for baseball.
Professional baseball career
Minor Leagues
Szczur signed a contract with the Chicago Cubs organization, which drafted him in the fifth-round of the 2010 Major League Baseball Draft. He received a $100,000 signing bonus, with an additional $500,000 if he declined to attend the NFL combine and made a written commitment to baseball before February 10, 2011. He was assigned to the club's short season Class-A team, the Boise Hawks, and first appeared in uniform July 8, 2010. He was then promoted to the club's mid-A team, the Peoria Chiefs on July 27, 2010. He hit.347 in 25 games in 2010. After the 2010 season, Szczur committed to baseball and signed a $1.5 million deal with the Cubs in January 2011. As he was released from his initial contract and signed a new contract to receive the bonus, he would have been eligible in the 2011 Rule 5 draft if not added to the Cubs' 40 man roster. On July 9, 2011, Szczur was assigned to the Class A-Advanced Daytona Cubs roster. On July 27, 2012, Szczur was promoted to the Double-A Tennessee Smokies. He began the 2014 season with the Triple-A Iowa Cubs before being promoted to the Major League roster.
Chicago Cubs
On August 16, 2014, Szczur was called up to the Cubs. He made his debut with the Cubs the next day. Szczur recorded his first Major League hit on August 21 against the San Francisco Giants and his first career home run on September 13 against the Pittsburgh Pirates Szczur split time during the 2015 season between Triple-A and the Majors, ultimately being called up by the Cubs on seven occasions. On April 29, 2016, Szczur hit his first Major League grand slam against the Atlanta Braves in the 8th inning, putting the Cubs up 6–1. In 2016, Szczur played 107 games batting.259 with five home runs and 24 RBI. Szczur made no appearances during the Cubs World Series run nor was he on the World Series roster.
San Diego Padres
Szczur was designated for assignment by the Cubs on May 6, 2017. The Cubs traded him to the San Diego Padres for RHP Justin Hancock on May 8. He declared free agency on October 2, 2018. In 2018 he batted.187.
On December 14, 2018, Szczur signed a minor league contract with the Arizona Diamondbacks. He elected free agency on November 7, 2019.
Philadelphia Phillies
Szczur signed a minor league contract with the Philadelphia Phillies on December 13, 2019, with an invite to major-league spring training camp. Szczur was released by the Phillies organization on June 28, 2020.
Personal
In 2009, Szczur donated bone marrow to a 15-month-old Ukrainian girl named Anastasia battling leukemia. Szczur essentially saved the girl's life given the severity of her condition and how hard it would have been to find another person that was a match for bone marrow. He met the healthy 4-year-old girl and her parents via Skype using a translator who was present at Anastasia's house. It was documented in E:60 Risking it All, which is one of ESPN's E:60 presentations. Szczur and his wife, Natalie, were married in November 2014 in Philadelphia, Pennsylvania. They have one child, Matt Jr.