The 31-year-old attacker has suffered a serious groin injury and he will be sidelined for a lengthy spell along with 18-year-old Kyle Munro, who is out for a similar length of time with a fractured wrist.
Rice said: "David and Kyle will miss at least three months each, David probably a bit more.
"It’s a huge blow. David is a special talent and young Kyle, it’s his first full season with us.
"It’s the same at every club," said Rice, who will have Jamie Hamilton and Andy Winter back in contention for Saturday’s trip to St Mirren after their spell of self-isolation.
"When something happens to one player the opportunity arises for someone else to step up.
"Ronan Hughes came off the bench last week, replaced David and got a couple of goals and played 75, 80 minutes at Aberdeen so the opportunity is there."