We present an experimental noise characterization of a miniature single-beam absorption-based optically-pumped magnetometer with a noise floor of 7 fT/Hz1/2 operating in the spin-exchange relaxation-free regime. We experimentally evaluate noise arising from the laser intensity, laser frequency, laser polarization, cell temperature, and magnetic field coils used for the phase-sensitive detection of the magnetometer signal. We find that noise in the range between DC and 30 Hz is a result of noise sources coupling to the atoms in a manner similar to a magnetic field, while the noise at frequencies above 30 Hz is mainly due to laser intensity noise. Our results place an upper limit on the noise sources for our system that matches well with the noise spectrum of the magnetometer at frequencies above 5 Hz.