We report the first detection of a magnetic field in a star of the FS CMa type, a subgroup of objects showing the B[e] phenomenon. These stars are surrounded by an extended circumstellar medium, which is responsible for emission lines from both permitted and forbidden transitions, a large infrared excess due to dust, and a very complicated variability. The split of magnetically sensitive lines in the spectra of IRAS 17449+2320 unexpectedly revealed a strong magnetic field with strength of 6.2+/-0.2 kG. Our discovery indicates the importance of considering magnetic fields in studies of FS CMa stars, whose evolutionary status is still unknown. We found that IRAS 17449+2320 has an effective temperature of ~10,000 K. Several spectral lines affected by the circumstellar medium (e.g., O I 7772–7775 AA, Balmer lines) regularly exhibit redshifted absorption components with a period of 36.13 days. The same periodicity shows up in the equivalent width of the Halpha line. The analysis of our data suggests three possible scenarios for the nature and evolutionary status of the object: i) a magnetic A-type star primary with a hot dwarf secondary, ii) a binary merger, or iii) a magnetic Ap star near the terminal age main sequence. The latter one may represent an object which has been sought for decades and fills the gap in the observations and theory of magnetic Ap stars.