Konta, seeded 11th, broke 21st seed Garcia in the fourth game of the first set and appeared on course for a place in the last 16.
But Garcia broke in the second to level the match and dominated the third-set tie-break, winning it 7-1.
Garcia will now face Italy's Roberta Vinci or Svetlana Kuznetsova of Russia.
Konta's defeat summed up a disappointing weekend for British tennis which saw world number one Andy Murray make a shock second-round exit to qualifier Vasek Pospisil and GB number two Dan Evans lose at the same stage to Japan's Kei Nishikori.
Briton Kyle Edmund faces second seed Novak Djokovic late on Sunday.
Garcia, who was once described by Murray as a future world number one, showed impressive resilience to recover from a set down against Konta and sealed her win and a place in the last 16 with a powerful cross-court backhand.
BBC tennis correspondent Russell Fuller at Indian Wells
Konta played without her usual fluency and, although she served better in the final set, she could not take any of three break points and was outplayed emphatically by Garcia in the tie-break.
The best part of four weeks off tour resting a foot injury may explain some of the rustiness, and - like Andy Murray - Konta now has virtually two weeks of practice stretching ahead of her before she plays her first singles match in Miami.