Norrie took the court on a sweltering afternoon in Paris and kept in touch with Vallejo for much of the first set.
However, the Briton struggled to move after missing four set points in a tight tie-break and going a break down at the start of the second.
Norrie called for the doctor and the trainer after losing his serve, pointing at his rib as he sat in the shade.
He told his team “every serve is a struggle” but attempted to continue, before ending proceedings midway through his next service game.
Even though Norrie believed he had enough to compete “at 20%”, he did not want to risk further damage with Wimbledon around the corner.
Norrie will return to London on Wednesday and go for a scan to determine the extent of the issue.
However, the 2022 Wimbledon semi-finalist remains confident he will be fit to start the British grass season at Queen’s in a fortnight.
“It’s far better not to exacerbate the injury problem and get back to the UK, have rest and treatment on it, and then start building up to Wimbledon,” former British number Annabel Croft said on BBC Radio 5 Sports Extra.
“We’ve heard from [Novak] Djokovic that his body doesn’t respond as well as it used to and into his thirties it was getting more difficult for his body to respond.
“This sport is so demanding and I can see why Norrie would have overtrained.”