The Austrian sprawled on his stomach on Court Two as he received a deep-tissue back massage from the trainer before the start of the third set.
The trainer then rolled Thiem on to his back to manipulate his shoulders but the intervention failed to have the desired effect and the seventh seed called it quits after losing the next two games.
Baghdatis was leading 6-4 7-5 2-0 when Thiem retired 97 minutes into the contest.
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While seven men retired within the first two days of the 2017 tournament, Thiem became the first man to quit mid-match this week.
Last year's spate of retirements forced a rule change which means players who withdraw in the opening round with a pre-existing injury risk losing all of their prize money, which for first-round losers this year is 39,000 pounds ($51,000).
(Reporting by Pritha Sarkar, editing by Ed Osmond and Clare Fallon)
