Dravid was hit on the nose by a bouncer from left-arm paceman Rudra Pratap Singh during practice but an X-ray ruled out a fracture.
The team's administrative manager Surendra Bhave said Dravid's injury was not serious and that he should recover in the next 48 hours.
"The ball hit the visor of Dravid's helmet. He suffered a nose trauma. It is not serious," he told reporters.
"The X-ray showed bruises and he has been advised 24-hour rest. He should be back in action in the next 48 hours," he added.
The Indian team are slated to leave on Monday for neighbouring Bangladesh for their tour which includes three one-dayers and two Tests. The first one-dayer is on May 10.
India were hit by another injury scare on Wednesday when star batsman Sachin Tendulkar suffered a right ankle sprain. Also middle order batting mainstay Laxman is down with gastroenteritis.
Tendulkar has since recovered and has been seen taking part in net practice.
India's tour of Bangladesh has assumed significance after Dravid's men lost to the minnows in the recent World Cup, a defeat which eventually led to the team's early ouster from the premier competition.