Thiem, who missed the second half of last season because of a wrist injury, arrived at Roland Garros on a six-match losing streak.
The Austrian was totally out of sorts once again on Court Simonne-Mathieu and Colombian Dellien capitalised, winning 6-3 6-2 6-4 on Sunday.
A two-time runner-up at the clay-court grand slam in Paris, Thiem has only won one set in seven matches since making his comeback – and that was at an ATP Challenger Tour event in Marbella in March.
The 2020 US Open champion racked up 42 unforced errors and did not have a solitary break point on another difficult day.
The 28-year-old had a first-serve success rate of only 59 per cent as world number 87 Dellien moved through to round two at Roland Garros for only the second time.
Thiem struck 29 winners to Dellien's 15, but the former world number three was broken four times as he crashed out.