The Red Sox placed Hill on the bereavement list Tuesday, Steve Hewitt of the Boston Herald reports.
Though he was able to make his scheduled start in Monday's loss to the Twins, Hill will take some time off to be with his family following the death of his father late last week. Hill will have to spend a minimum of three days on the list, but the expectation is that he'll rejoin the team before his next turn in the rotation comes up Saturday at Tampa Bay.