The Dalai Lama fled Tibet in 1959
Doctors at Bombay's Lilavati hospital, where the 66-year-old leader was admitted on Sunday, said he was in good spirits and could soon be discharged.
Further tests were expected later on Monday.
The Dalai Lama's personal secretary, Tenzin Tethong, said the infection was now "under control."
"Since the start of treatment with antibiotics ... some visible improvement has already been confirmed," he said. "Further improvement is expected."
Festival postponed
The Dalai Lama had been in the eastern state of Bihar for a Buddhist festival when he complained of stomach problems.
A team of doctors examined him and advised him to undergo more tests in Bombay.
He took a flight to Bombay from Patna airport, where he arrived by helicopter from a Buddhist monastery in Bodhgaya.
Witnesses said the Dalai Lama walked unaided onto the plane and did not speak to reporters.
The Dalai Lama's illness has led to the ceremonies being called off at the 10-day Kalchakra (Wheel of Time) festival in Bodhgaya, which began last week.
At a ceremony postponed last Thursday, the Dalai Lama told followers he would not be able to sustain rituals which required him to sit still for long periods.
Tens of thousands of people had converged on Bodhgaya for the festival, the largest Buddhist gathering in the world.
Indian exile
Devotees expressed disappointment that the Dalai Lama had been unable to take part and prayed for a swift recovery.
The Dalai Lama's personal physician, Tsen Dorji Sadutshang, was quoted on Sunday as saying the acute abdominal pains had first appeared in the middle of December and that the problem had persisted despite treatment with Tibetan and Western remedies.
The Dalai Lama fled Tibet in 1959 with thousands of supporters following a failed uprising against China.
Since then, he has headed a government-in-exile in the northern Indian town of Dharamsala.
He was awarded the Nobel Peace Prize in 1989 for his non-violent struggle against Chinese rule.