Pant fell asleep at the wheel of his Mercedes while driving alone and collided with the central reservation on a road in Uttarakhand, northern India, according to news channel NDTV.
The 25-year-old was being treated in Saksham Hospital Multispecialty and Trauma Centre for cuts to his forehead as well as injuries to his knee, wrist, ankle and toe before being transferred to Max Hospital in Dehradun.
The Board of Control for Cricket in India (BCCI) said in a statement: "India wicket-keeper Rishabh Pant met with a car accident early on Friday morning near Roorkee, Uttarakhand.
"He was admitted to Saksham Hospital Multispecialty and Trauma Centre where he was treated for impact injuries.
"Rishabh has two cuts on his forehead, a ligament tear in his right knee and has also hurt his right wrist, ankle, toe and has suffered abrasion injuries on his back.
"Rishabh's condition remains stable, and he has now been shifted to Max Hospital, Dehradun, where he will undergo MRI scans to ascertain the extent of his injuries and formulate his further course of treatment.
"The BCCI is in constant touch with Rishabh's family while the Medical Team is in close contact with the doctors currently treating Rishabh.
"The Board will see to it that Rishabh receives the best possible medical care and gets all the support he needs to come out of this traumatic phase."
Pant, captain of Indian Premier League (IPL) side Delhi Capitals, has made 33 Test appearances for India and has played in 30 one-day internationals.
He has also made 66 T20 international appearances and was the youngest player to debut for India in the format at the time, aged 19 years and 120 days in 2017.
Pant made a top score of 93 as India secured a 2-0 Test series win against Bangladesh on Christmas Day.
BCCI honorary secretary Jay Shah tweeted: "My thoughts and prayers are with Rishabh Pant as he fights his way back to recovery.
"I have spoken to his family and the doctors treating him. Rishabh is stable and undergoing scans. We are closely monitoring his progress and will provide him with all the necessary support."