The Cubs acquired Hart from the Orioles last December in a trade that sent INF/OF Freddie Bynum to Baltimore.
"For the most part, he's kept us in games," Tennessee manager Pat Listach recently said of Hart. "He's got a really good slider and a good sinker. You take away some bad starts and he's had some pretty good numbers."
Hart is expected to make his first start with Iowa Friday in Omaha.
In a corresponding move, left-hander Ryan O'Malley was sent to Tennessee. The 27-year-old was 3-8 with a 7.58 ERA in 18 starts at Iowa.
No additional roster moves are known at this time.