"Going to see Lance Naik Hanumanthappa Koppad, with prayers from the entire nation," Modi tweeted just before visiting the hospital.
Koppad was flown here from Siachen Glacier this morning in a special air ambulance and admitted to the Research and Referral Hospital.
His condition is critical but stable and he is undergoing various tests in the hospital, army sources said.
Hanumanthappa, who hails from Karnataka, was found alive yesterday, buried under 25 feet of snow for six days after an avalanche hit his post at the altitude of 19,600 feet close to the Line of Control (LoC) with Pakistan.
The temperature at that altitude was minus 45 degrees Celsius.
Nine other personnel at the post, including a Junior Commissioned Officer (JCO), of Madras Regiment have died, according to Lt Gen D S Hooda, Northern Army Commander. "Five bodies have been recovered so far and four bodies have been identified," he has said.