Skube attended Simi Valley High School, and the University of Southern California before turning professional.

During the 1979 Major League Baseball draft, the Milwaukee Brewers selected Skube in the 13th round.

Over his minor league career, Skube batted .276 with 634 hits, 140 doubles, 24 triples, and 80 home runs.

[7][8] Skube made his professional baseball career debut in 1979 with the Class-A Burlington Bees in the Milwaukee Brewers minor league organization.

After the season, Skube won the Eddie Mulligan Award, which is bestowed to the top rookie in the California League.

At the end of the season, the Milwaukee Brewers purchased Skube's contract, adding him to their 40-man roster.

[13] He attended spring training with the Milwaukee Brewers in 1982, and was said to be the leading candidate for the back-up outfielder position on the major league roster.

In late-August, there were rumors that the Brewers had traded Skube to the Houston Astros in a deal for Don Sutton.

[17] He made his MLB debut against the New York Yankees on September 17, pinch-hitting for designated hitter Roy Howell in the eighth inning.

He made his season debut on April 10, against the Kansas City Royals, getting no hits, one run scored, and one RBI in two at-bats.

On the season with the Brewers, he played in 12 games, batting .200 with two runs scored, five hits, one double, one triple, and nine RBIs.

[21] Skube commented that during the off-season, he had trained harder than ever before, and hoped to make the major league roster.

With El Paso, he batted .312 with 63 hits, 17 doubles, two triples, and six home runs in 56 games played.

In late-June, Skube was promoted to the Triple-A Vancouver Canadians, where in 61 games he batted .267 with 56 hits, 13 doubles, four triples, and nine home runs.

In 2003, Skube was involved in a baseball camp for the Milwaukee Brewers, which included former players Ken Sanders, Moose Haas, Rob Deer, Del Crandall, Bill Schroeder, Dale Sveum, and Lou Klimchock.

In 2007, Skube was hired as the hitting coach for the Class-A Fort Wayne Wizards of the Midwest League.

[32] He was hired as the hitting coach for the Class-A Lake Elsinore Storm of the California League in 2010.