O'Driscoll sustained a hyper-extended elbow in Sunday night's 32-17 victory over Namibia and appeared for the post-match press conference with his right arm in a sling.
But the discomfort has eased and the Lions centre will lead Ireland, who name their team on Tuesday afternoon, in their second World Cup group match.
A statement from the Irish camp read: "Brian's injury has settled down overnight and following treatment.
"The injury did not require an x-ray but will continue to be monitored during training this week.
"It will not rule him out of selection for the game against Georgia."
There was also an encouraging update on Ronan O'Gara and Marcus Horan, who sustained foot and back injuries respectively, with the Munster duo set to be included in the team for Georgia.
The statement continued: "Ronan bruised his left foot against Namibia but this has also improved over the last 24 hours and he is no longer an injury concern.
"He is expected to take part in training tomorrow. Marcus Horan received a knock to his upper back and has some muscular bruising in this area.
"He will not take part in training tomorrow, but is expected to be available for the weekend's game."
In a final fitness boost for Ireland, Shane Horgan was given the all clear to make his first appearance in the tournament.
Horgan suffered a knee ligament strain while warming up before last month's clash with Scotland but has completed his rehabilitation on schedule.
The statement said: "Shane Horgan will take a full part in training this week. His recovery means he will be available for Georgia."