His father Felipe, who managed Moises with the Expos from 1992 to 1996 and the Giants from 2005 to 2006, as well as uncles Matty and Jesús, and cousin Mel Rojas, all had long careers in Major League Baseball.
Alou suffered a severe ankle injury in 1993 that would rob him of his speed and force him to become strictly a corner outfielder. He recovered in 1994, hitting .339 and hit the game-winning hit in the year’s All-Star Game. For the next two seasons, he would enjoy success at the plate in Montreal, although surgery to both shoulders prematurely ended his 1995 season
Prior to the 1997 season, Alou signed as a free agent with the Florida Marlins, where he led the team with 23 home runs and 115 RBIs. The Marlins made the playoffs as a wild card team, and defeated the San Francisco Giants in the National League Divisional Series, and then the Atlanta Braves in the National League Championship Series, before going to the World Series, which Florida won in seven games. Alou led the team by hitting .321 with three home runs and nine RBI in the World Series (although, pitcher Liván Hernández, by virtue of his wins in Games 1 and 5 was named the Series Most Valuable Player instead).
Before the 1998 season, the Marlins traded Alou to the Houston Astros. In his first season with the team, Alou hit a career-high 38 home runs and drove in 124 runs while leading the Astros to a franchise record 102 wins. However, he tore his ACL in a treadmill accident in the offseason, and missed the entire 1999 season. Once recovered, he returned to the Astros lineup to hit .355 in 2000 and .331 in 2001, while driving in at least 108 runs in each season. After the 2001 season, the Astros did not offer Alou a new contract, making him a free agent.
In December 2001, he inked a 3-year, $27 million contract with the Chicago Cubs.
In 2002, Alou again ended up on the disabled list at the start of the season, and once healthy, he hit .275 and 15 home runs. After the 2002 season, Alou, hired a personal trainer and dedicated himself[vague] to return to his old form. In the 2003 season, Alou batted over .300 for most of the season while driving in runs as he used to[quantify], before a late season slump dropped his season batting average to .280, with 22 home runs and 91 RBIs. Alou went on to lead the team in average in its two series against the Atlanta Braves and Florida Marlins.
In Game 6 of the National League Championship Series against the Florida Marlins that year, Alou was involved in the Steve Bartman incident, in which a Cubs fan named Steve Bartman deflected a foul ball landing one row into the stands, preventing Alou, who reached into the stands, from attempting to catch the ball for an out that could have been the second out of the 8th Inning. However, the Marlins went on to score eight runs in the inning, which the Cubs had led 3–0. The Cubs, who had led the series 3–2, lost the game 8–3 and eventually lost the series in seven games. Alou openly admitted later in interviews that while he was frustrated at the moment, he could not have made the catch anyway. Later he denied making such a statement and said if he had, it was only to make Bartman feel better.
In 2004, Alou set new career highs in home runs (39) and doubles (36), while driving in 106 runs. However, the Cubs missed the playoffs after losing seven of their last nine games. The Cubs refused to offer arbitration and let him go, citing numerous fights with umpires whom he claimed had a vendetta against him
In October 2004, Alou announced that he had talked to his father, Felipe, about possibly playing for him and the Giants next season. In December 2004, he signed a one-year deal with the Giants worth 13.5 million, with a player option for a second year. Alou was expected to regularly play in right field for the first time since 2001, but due to injuries to left fielder Barry Bonds, he started most games in left field. Alou had stated that he would retire if the Giants won the World Series in 2005. They did not, and Alou exercised his option and stayed with San Francisco in 2006 season, hitting 22 home runs and 74 RBI.
On November 20, 2006, the New York Mets signed Alou to a one-year contract worth $7.5 million with a club option for 2008. After hitting .318 in his first month as the regular left fielder, Alou suffered a torn quadriceps muscle, and was forced out until August. Upon his return, Alou led the Mets with a .345 batting average and had a 30-game hitting streak. The streak was the longest streak of the 2007 season, was the longest hitting streak by a player over age 40, and broke the Mets’ overall and single-season hitting streak records.
On March 5, 2008 Alou underwent hernia surgery and missed the start of the 2008 season. On July 9, Alou suffered a torn right hamstring playing in the outfield for AA Binghamton in Norwich, Connecticut. Mets general manager Omar Minaya stated in a press conference the following day that Alou will likely need surgery and miss the remainder of the 2008 season, which ended his career.