Duensing was placed on the list before Monday's season opener. His wife, Lisa, gave birth to their son Boston Matthew on Tuesday morning in Omaha, Neb.
Tonkin pitched one scoreless inning in Wednesday's loss to the White Sox, allowing one hit and striking out one.
Duensing pitched in 73 games last season for the Twins, all in relief. He was 6-2 with one save with a 3.98 ERA and 1.475 WHIP in 61 innings. In five seasons with the Twins, Duensing is 34-33 with a 4.20 ERA and 1.391 WHIP in 237 games (61 starts).