Blackburn, 30, struggled in 2012, posting a 7.39 ERA in 19 starts. The sinkerballer also struck out 42 and walked 26 in 98 2/3 innings.
He was eventually outrighted off the 40-man roster on Aug. 20 and sent to Triple-A Rochester, where he finished the season.
Blackburn is owed $5.5 million next season in the final year of a four-year, $14 million deal signed before the 2010 season. The Twins also hold an $8 million option for 2014.
Blackburn has a career 4.85 ERA in 818 2/3 innings over six years with the Twins. He's struggled over the last three years, logging a 5.56 ERA after posting a combined 4.04 ERA over the previous two seasons.