He played in Major League Baseball (MLB) for eight seasons (1961; 1964–1967; 1969–1972) for the Detroit Tigers, Kansas City Athletics, New York Mets, Minnesota Twins, Washington Senators and St. Louis Cardinals.

Born in Scranton, Pennsylvania, he stood 6 feet 2 inches (1.88 m) tall and weighed 180 pounds (82 kg).

Not known for his hitting ability, Grzenda once grounded out to third base in RFK Stadium and received a standing ovation.

On September 30, 1971, he became the last pitcher in the franchise's tenure at Washington, D.C., getting two outs in the top of the ninth inning before fans, knowing the team would be leaving for Dallas–Fort Worth after the season to become the Texas Rangers, stormed the RFK Stadium field, causing a forfeit.

As a fielder, Grzenda was charged with no errors during his eight-year career for a perfect 1.000 fielding percentage (6 putouts, 66 assists).