Chamberlain, 22, left the team after Sunday's game to return home, where his father, Harlan, was listed in critical but stable condition at Saint Elizabeth Regional Medical Center in Lincoln, Neb.
The right-hander has been placed on the Major League bereavement list, making him ineligible to play for a minimum of three games. The Yankees play the Red Sox in New York on Wednesday and Thursday.
"Of course he wants to be here," Girardi said. "He understands what he needs to do as a son. Joba is very mature and Joba has been through a lot in his lifetime. You only have so many days with the people that you love, so you've got to make sure you're where you're supposed to be at the right times."
Girardi said that he spoke with Chamberlain on Tuesday and that the elder Chamberlain was doing "a little better," but that more tests still needed to be conducted.
A retired prison counselor, the 55-year-old Chamberlain has coped with health issues for most of his life. He was stricken with polio as a child and utilizes a motorized scooter for transportation.
"Joba is by his side and just praying that he gets better," Girardi said. "He's doing OK. He understands that it's important for him to be there. He's taking care of Pops."
There is no timetable for Chamberlain's return to the Yankees. The club recalled right-hander Jonathan Albaladejo from Triple-A Scranton/Wilkes-Barre on Monday to take Chamberlain's place in the bullpen.
"He can take as long as he needs to take," Girardi said. "There's nothing more important."
That creates an issue for the Yankees on the field, however. As he was during the second half last season, Chamberlain was a trusted and dominant cog in New York's bullpen earlier this month, throwing 5 1/3 scoreless innings and striking out six in four appearances.
With Chamberlain removed from the roster, the Yankees need to find other ways to get the ball to closer Mariano Rivera. Had the Yankees gone forward with Chamberlain as a starting pitcher this year, an idea they originally flirted with, LaTroy Hawkins and Kyle Farnsworth would have filled the eighth-inning mix.
Though the team considers Billy Traber a left-handed specialist, Girardi said that right-hander Brian Bruney -- who allowed two home runs in a 1 1/3-inning appearance against the Rays on Monday, but has a 2.16 ERA in six appearances -- could find his way into the arrangement as well.
"Other guys need to step up," Girardi said. "That's the reality of baseball -- it happens all the time. [Derek] Jeter went down and [Alberto] Gonzalez stepped up. Jorge [Posada] went down and [Jose] Molina stepped up. It's no different when it's a pitcher. Someone has to step up and I expect our guys to do it."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.