Chappell, who quit as coach after the team's disastrous first round exit in the World Cup, had postponed his flight after feeling unwell.
Chappell waved to a horde of journalists outside Bombay Hospital in the western city of Mumbai on Saturday as he left the building following the tests.
Doctors would examine the results "and then decide whether Chappell is fit enough to fly out of the city," hospital spokesman Ashish Kumar Tiwari said, quoted by PTI.
"He was brought to the hospital and has been receiving a checkup at the hospital .... There is presently no cause for concern," Tiwari said.
The Australian underwent renal, liver, lipid and blood checks, Tiwari said.
"I came for a routine check-up and am fine," Chappell said in a statement.
There were no further details.
Chappell and his wife, Judy, had been planning to fly to Singapore later on Saturday for a short break before heading home to Australia.
Chappell had postponed the journey by a day after he felt unwell, PTI said.