After graduating from Kennedy High School in Chicago, Illinois, Hickey played college baseball for the University of Texas–Pan American.

His best career season was in 1984, when he went 13–5 and had a 1.81 ERA in 49 relief appearances for the Single-A Appleton Foxes who were the champions of the Midwest League that year.

Starting in 1996, Hickey became the pitching coach for two seasons at the Houston Astros' Double-A affiliate, the Jackson Generals, where his staff led the Texas League with 939 strikeouts in 1997.

In his first year with Houston, he helped the pitching staff which included Roger Clemens, Brad Lidge, Roy Oswalt and Brandon Backe advance to the 2004 National League Championship Series.

In 2005, the Astros advanced to the World Series, with Clemens (1st), Andy Pettitte (2nd), and Roy Oswalt (7th) in the National League in ERA.

On November 18, 2006, Hickey was announced as the new pitching coach for the Tampa Bay Rays, replacing Mike Butcher.