Benitez leaves on compassionate leave
Birmingham manager Alex McLeish said on the club's website: "We are aware of the bad news concerning Christian's father and had no hesitation in granting him permission to travel home.
"He has settled in well and has already shown that he is a key figure for us, but we fully understand his desire to be with his family at this time."
Benitez, who joined Birmingham for a club record fee that could rise to 7.7 million pounds in July, has made eight appearances for the club so far without scoring. He is likely to miss Saturday's league match against Burnley.