The Twins promoted Matthews from Single-A Fort Myers to High-A Cedar Rapids on Sunday.
The 23-year-old right-hander was advanced to the Midwest League after he submitted a 2.56 ERA, 0.92 WHIP and 53:5 K:BB across 38.2 innings with Fort Myers. Matthews is regarded as one of the better ams in the lower levels of the Twins' farm system.