Draper, ranked 28th in the world, has been cautious during a return from an arm injury and pulled out of the recent Monte Carlo Masters before the tournament.
He was absent for six months because of a bruised bone in his left serving arm, before returning to competitive action in February.
“Sad to retire in Barcelona. I’ve tried hard these last months to stay positive and give my all,” Draper posted on Instagram.
“It will take time but I will work my way out of this. Thank you for all the support throughout this process.”
The Barcelona Open was Draper’s fourth event since he made his comeback.
Etcheverry said: “I like how he plays – he’s a great fighter.
“Hopefully he can recover as soon as he can to get back on tour because the tour likes him.”
Cameron Norrie, who replaced Draper as British number one last month, beat Switzerland’s Stan Wawrinka 6-4 6-7 (5-7) 6-4 to reach the second round.
Norrie served for the match at 5-4 in the second set but let the 41-year-old back into the contest before he got himself back on track in the deciding set.
“I put myself in a winning position serving at a set and 5-4 up,” said 30-year-old Norrie, who will play Ethan Quinn of the US next.
“I played a little tentatively in two shots and then I was very tight in the tie-break. I probably should have won it then, but credit to him.
“I played at a really good level in the third set.”
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