Drafted by the Florida Marlins in the 6th round of the 2008 MLB Draft from Westlake High School in California. Spent five years in the Marlins organization, starting in the Florida Gulf Coast League in 2008 at the age of 18 and threw in three games, starting twice, and held a 5.40 ERA. In 2009, Johnson advanced to single-A with Greensboro and tallied a 6-7 record with a 4.83 ERA in 20 starts and 91.1 innings pitched. Johnson struck out 52, while walking 47.

In 2010, he was sent to high-A ball in Jupiter where he held a 2-12 record with a 6.18 ERA in 26 appearances, including 15 starts in 94.2 innings pitched. He struck out 60 and walked 52. In 2011, Johnson stayed in Jupiter, throwing in 33 games out of the bullpen and held a 7.51 ERA with an 0-4 record in 56.1 innings pitched. Johnson walked 34 and struck out 30.

In his final year with the Marlins organization, he spent a short time with the Gulf Coast League Marlins in rookie ball, appearing in just seven games with two starts, holding a 9.00 ERA with a 1-1 record.