Klinger, 36, has hit three centuries in 10 Championship innings so far this season, averaging 94.83.
His side have five Division Two matches left in 2016, but he is likely to miss September's trip to Northamptonshire and the last game, the visit of Sussex.
"We have a baby due in mid-October," the Australian told BBC Radio Bristol.
"Once it gets within that four-week period, I can't be here in case the baby comes. I'd struggle to make it with a 24-hour flight back home if she went into labour. I'll leave on the 11th (of September)."
Gloucestershire captain Michael Klinger is set to miss their final two County Championship matches of 2016 as his wife is expecting a baby in October.