Both central defenders are nursing knee injuries following the 2-2 draw against Sheffield Wednesday on Saturday.
O'Brien has been troubled by discomfort in his knee in recent weeks. He was named in the starting XI at Hillsborough but pulled out during the warm-up.
Derby turned to Buxton, who had not played in nine weeks due to knee ligament damage. He managed to get through the 90 minutes but tweaked the same knee that had kept him out.
James O'Connor, who can play anywhere along the back four, would usually come in and deputise but he is definitely out with a knee injury of his own.
Manager Nigel Clough hopes one of the injured defenders can emerge from the treatment room as the Rams look to extend their three-match unbeaten league run.
"We're not sure who will play centre-half with Richard Keogh at this moment," said Clough. "Jake has tweaked his knee again, the same knee he has been out with, and so between him and Mark O'Brien we are not sure who will make it. Jimmy O'Connor will not be right for Tuesday."
If Clough finds himself short, he could switch John Brayford from right-back and bring in Kieron Freeman.
Valentin Gjokaj, who has yet to start a first-team game, was on the bench on Saturday and is an option, along with fellow youngster Tom Naylor who is back at Pride Park following his three-month loan spell at Bradford.
Elsewhere, forward Jamie Ward is expected to be fit despite coming off towards the end against Wednesday due to cramp in his calves.