American 12th seed Madison Keys also brushed aside Great Britain's Ashleigh Barty 6-3, 6-2.
Konta collected just two singles victories during the clay-court season in the lead-up to Roland-Garros and has now fallen at the first hurdle in Paris for three years running.
"I tried very hard and gave myself a big chance".
The British number one has made no secret of the fact clay is her least favourite surface and, following Tuesday's loss, she has still to win a match in the main draw at Roland Garros.
The world No. 8 was in complete control of the match after the first set, which she took 6-1, but failed to find the breakthrough in the second and lost it on a tiebreak before going on to lose the third. "She's an unorthodox player, but uses the best of her ability to her advantage".
Hsieh had won just twice at tour level this year and appeared to be heading for a swift exit as Konta raced through the opening set.
But while disappointed with her showing at the French Open, a determined Konta refused to press the panic button.
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Hsieh has a second-round clash to look forward to, and could barely contain her delight.
"My expectations are never results-orientated".
"(After the first set) I created opportunities, (but) I didn't do well enough in converting them.
"Obviously, I like to be involved in a tournament for as long as possible, and I would have liked to have been involved here longer".
- Fifth seed Elina Svitolina of Ukraine beat Yaroslava Shvedova of Kazakhstan 6-4 6-3 in the first round.
Konta, who is now the world number eight, then failed to convert any of her four break points at 5-4 before netting a return to hand Hsieh the match. Townsend toppled Japanese qualifier Miyu Kato 6-4, 6-0 in her first-round match.