Gwen Stefani -- Cops Scramble After Obsessed Fan's Creepy Message

Gwen Stefani was literally on pins and needles after an obsessed fan threatened to meet her at a Korea Town acupuncture clinic ... forcing her to call in cops.

Law enforcement sources tell TMZ ... the singer's been dealing with this fan for awhile, but things took a terrifying turn Monday when he sent her a slew of messages which said he'd be waiting at the clinic, waving from a nearby spot.

A rattled Stefani -- who had her 1-year-old son Apollo with her -- called police who spotted a suspicious man and questioned him. Turns out, it was just some random guy who happened to get some fresh air at the wrong time.

We're told investigators are still trying to track down whoever's sending the messages.