Rasmus has been mired in a 3-for-66 slump since July 2 and told reporters a few weeks ago he has been dealing with cholesteatoma, a growth of skin cells occurring behind the eardrum that causes damage. The Astros specified the injury as a cyst on Sunday.
The 29-year-old said he would eventually have to have surgery, though it's not known if he will undergo that while on the DL.
"That's certainly on a personal level for him, so I don't want to speculate or anything like that," Hinch said.
Hinch, who has seen infielder Luis Valbuena (right hamstring), pitcher Lance McCullers (right elbow sprain) and pitcher Luke Gregerson (left oblique) go on the DL in the past week, said his team will again be short-handed Sunday, with infielder Tyler White (knee) and outfielder Carlos Gomez (illness) also unavailable.