Cummins said Smith had recovered sufficiently from a dislocated finger to resume his position at number four for the match starting on Thursday.
Inglis misses out after scoring five and 12 in the only change following Australia's 159-run win in the Barbados series opener.
Smith dislocated his right little finger in last month's World Test Championship final and will be required to wear a splint for five weeks, Cricket Australia said.
However, the veteran came through a 30-minute batting session unscathed, along with some slips catching drills.
"He's ready to go, the finger held up well," Cummins told reporters.
"He was really happy, particularly batting."
Australia's XI for the second Test
Usman Khawaja, Sam Konstas, Cameron Green, Steve Smith, Travis Head, Beau Webster, Alex Carey, Pat Cummins (capt), Mitchell Starc, Nathan Lyon, Josh Hazlewood