Keane has an infection in his foot while McCarthy tweaked his hamstring at Chelsea in midweek and is set for a further two weeks out.
But the England centre-half is in line to be fit for Sunday’s visit of Watford to Goodison Park.
Unsworth explained: ”Unfortunately, Michael got a knock - a really bad gash - when we played Sunderland in the League Cup
“It has got infected and that infection has spread and it’s been really, really nasty so he’s been hospitalised.
“But we got some good news just before we got to the ground that there’s been a big, big improvement and hopefully he can be available for Sunday’s game.”
McCarthy’s 60 minute outing against Chelsea on Wednesday night had been his first start for the Blues in nine months.
Unsworth added: “Unfortunately, after the Chelsea game he got a little tweak. We got it scanned on Friday and there’s a little strain there.
“That’s going to be a couple of weeks [on the sidelines], which is disappointing because he’s a big player for us.”