Martic, a lucky loser ranked 30th in the world, battled through blustery conditions to secure a 6-4 7-5 victory over Boulter.
This marks Boulter’s second consecutive first-round defeat, following her early exit at the Birmingham Classic last week.
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Meanwhile, in the men’s draw, Liam Broady triumphed over Jan Choinski 6-3 6-4 in an all-British encounter.
Broady secured the first set with just one break and went an early break up in the second.
Although Choinski forced the setback on serve, Broady instantly responded with a break of his own and served out the match.
He will now face Sweden’s Mikael Ymer in the last-16 tie.
Boulter, who received a wildcard to play at Wimbledon next week after her Nottingham Open triumph, started strong against Martic but lost her serve in the fifth game due to a long forehand.
Despite four break points for the Briton in the next game, Martic, who has previously reached the fourth round at Wimbledon three times, ultimately clinched the first set.
The wind made serving difficult for both players, and Boulter found herself having to save two break points at 5-5.
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She managed to save the first with a floated drop shot and the second with a stunning forehand down the line under pressure.
However, Boulter’s good work was undone as she smacked a backhand into the net, giving Martic a crucial break that allowed her to serve out the match.
