A right-handed pitcher, Carrasquel had a fine fastball, which he complemented with an effective knuckleball and a decent curve. He started his major league career with the Washington Senators in the American League on April 23, 1939.

Although World War II was officially over and baseball's finest players were back in their familiar ranks, tranquility no longer had a place in the majors. The new Mexican League, headed by millonaire Jorge Pasquel, had lured a cluster of bigleaguers. On January 2, 1946, the Chicago White Sox bought Carrasquel's contract from the Senators. He rejected the deal and fled to play in Mexico, signing a three-year contract - the first shot in the cross-border disputes that would dominate baseball even more than the return of the war veterans. There were others several players that fled to Mexico, including outfielder Danny Gardella, pitchers Sal Maglie and Max Lanier and catcher Mickey Owen. Baseball Commissioner Happy Chandler sought a lifetime suspension for them, but his penalty was later reduced.

In 1949 Carrasquel returned to the majors and made only three appearances for the White Sox before being farmed out. When Chicago acquired his nephew Chico Carrasquel in that season, GM Frank Lane swapped Alex for reliever Witto Aloma, who acted strictly as an interpreter for the young Venezuelan shortstop.

In an eight-season major league career, Carrasquel posted a 50-39 record with 252 strikeouts, a 3.73 ERA, 30 complete games, four shutouts, 16 saves, and 861 innings pitched in 258 games (64 as a starter).