The 24-year-old Briton, who returned to action in February after six months out due to a niggling left arm injury, pulled up while trailing 1-4 in the deciding set of his meeting with Argentine Etcheverry to cast doubts on his fitness for the clay season.
"Sad to retire in Barcelona. I've tried hard these last months to stay positive and give my all," Draper, who tried to soldier on with taping below his right knee, said in a post on social media.
"It will take time but I will work my way out of this. Thank you for all the support throughout this process."
After an early exit in Dubai in February, Draper shook off the cobwebs to beat 24-times Grand Slam champion Novak Djokovic at Indian Wells but his title defence in the Californian desert ended in the quarter-finals against Daniil Medvedev.
The left-hander then suffered another early defeat in Miami and pulled out of Monte Carlo to protect his arm, but hoped to kick-start his campaign in Barcelona ahead of the French Open that will begin on May 24.
"I like how he plays, he's a great fighter," Etcheverry said of the former world number four, who has now slipped to 28th in the rankings.
"Hopefully he can recover as soon as he can to get back on tour, because the tour likes him."