Altherr was drafted by the Philadelphia Phillies in the ninth round of the 2009 Major League Baseball Draft out of Agua Fria High School in Avondale, Arizona. The Phillies pried him away from a commitment to the University of Arizona with a $150,000 signing bonus. He also received Division I scholarships for his basketball skills. He was assigned to the GCL Phillies, where in 28 games to finish 2009, he hit .214 with 1 HR and 11 RBI.
Altherr began 2010 back with the GCL team, where in 27 games, he hit .304 with 15 RBI and 10 SB, but he struck out 22 times to just 3 walks. He earned a promotion to Short-Season Williamsport on July 22. In 28 games with Crosscutters, he hit .287 with 10 RBI, and just 13 strikeouts to 8 walks. After the season, he was rated the Phillies 10th best prospect by Baseball America. Altherr began 2011 with Single-A Lakewood, but he hit poorly, hitting just .211 with 15 RBI and 12 SB in 41 games. By the time the New York–Penn League began in 2011, he was back with Williamsport, but he understood the demotion and worked to regain his confidence. He was an All-Star in 2011, and in 71 games with Williamsport, he hit .260 with 5 HR, 31 RBI, and 25 SB.
Altherr was given a second shot at Lakewood, and in 110 games, he hit .252 with 8 HR, 50 RBI, and 25 SB. He played mostly left field up to 2012, but he was used mostly at center field with Lakewood. He played 2013 with High-A Clearwater, where in 123 games, he hit .275 with 12 HR, 69 RBI and 23 SB, but he struck out 140 times.
Altherr played for the Germany national baseball team in the qualifying rounds for the 2013 World Baseball Classic. He played in the Arizona Fall League during the offseason in 2013. He was added to the Phillies 40-man roster on November 20, 2013. He played in the Arizona Fall League in 2013 with the Peoria Javelinas. In 12 games, he hit 9-45 (.200) with 3 RBI, 2 SB and 3 2B.
Altherr was set to begin 2014 with Double-A Reading, but he was sent to Clearwater before playing a game with Reading on April 13. However, after 7 games, he was quickly promoted back to Reading. He was hitting .245 in 52 games with 4 HR and 23 RBI, including hitting .417 with 9 RBI in his last 12 games, before he was promoted to Philadelphia.
On June 16, 2014, Altherr was recalled to Philadelphia to replace outfielder Tony Gwynn, Jr., who was placed on the bereavement list following the death of his father, Tony Gwynn. He made his major league debut that night, appearing as a pinch-hitter in the 12th inning against Atlanta. He flew out to center field, and was replaced by pitcher Antonio Bastardo in the lineup. He was optioned back to Reading on June 19.
After splitting the first four months of 2015 season between Reading and the Triple-A Lehigh Valley IronPigs, he was recalled to Philadelphia on August 18. The following day, he recorded his first Major League hit, an RBI double against Mark Buehrle of the Toronto Blue Jays. He hit his first major league home run that same game against reliever Bo Schultz.
On September 25, Altherr hit an inside-the-park grand slam off Jordan Zimmermann in an 8-2 win over the Washington Nationals, driving in Brian Bogusevic, Cameron Rupp, and Jerad Eickhoff. The grand slam was the 225th inside-the-park grand slam in Major League history, and the first since Randy Winn did so for the Tampa Bay Devil Rays in a 6-2 win over the New York Yankees on October 3, 1999. Altherr hit a second home run in the fifth inning of the game, becoming the first player to record a multi-home run game including an inside-the-park grand slam since Bob Brower of the Texas Rangers did so in a 13-3 win over the Oakland Athletics on June 21, 1987.
During spring training in 2016, Altherr tore a ligament in his left wrist, requiring surgery that caused him to miss the first half of the season. He was activated from the disabled list on July 28.
On September 18, 2017, in a 4–3 win over the Los Angeles Dodgers, Altherr hit a grand slam which was the first one ever given up by Clayton Kershaw, who was making his 288th regular-season start and had pitched 1,917 innings in 10 seasons.
Altherr was born in Landstuhl, Germany when his mother was stationed there as a member of the U.S. Armed Forces. His father is a former German professional soccer player. On November 20, 2016 Aaron married his girlfriend, Samantha Chavez.