Nicolino attended University High School in Orlando, Florida. Playing for the school's baseball team, he had a 4–2 win–loss record and a 1.95 earned run average (ERA) with 74 strikeouts in 44 innings pitched in his senior year. He committed to attend the University of Virginia on a college baseball scholarship. Projected as a third or fourth round pick in the 2010 Major League Baseball Draft, Nicolino expected to honor the commitment.

The Toronto Blue Jays selected Nicolino in the second round of the 2010 Draft, with the 80th overall selection. He signed with the Blue Jays for a reported $615,000 signing bonus, rather than enroll at Virginia.

Nicolino made his professional debut for the Vancouver Canadians of the Class A-Short Season Northwest League in 2011, posting a 5–1 win–loss record and a 1.03 ERA. The Blue Jays promoted him to the Lansing Lugnuts of the Class A Midwest League late in the season, and he pitched to a 1–1 record and a 3.12 ERA in three starts for Lansing. Nicolino returned to Lansing for the 2012 season. He had a 10–4 win–loss record with a Midwest League-best 2.46 ERA and 119 strikeouts in 124 ¹⁄₃ innings pitched. His teammates voted him as the Lugnuts' Most Valuable Player, and he was named to the Midwest League Postseason All-Star team.

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