Intrinsic thermal noise in optical fibers is an ultimate factor limiting the performances of fiber-based sensors and measurement systems. Therefore, it is important to have a thorough understanding of this kind of noise. However, the mechanism of the intrinsic thermal noise which has a 1/ fspectral density remains unclear so far. There are two theoretical models to explain the mechanism of this kind of noise: thermoconductive noise model and thermomechanical noise model. The thermoconductive noise model states that the noise is caused by diffusion of local entropy fluctuations associated with random spontaneous emission events, while the thermomechanical noise model says that the noise is caused by spontaneous fluctuations of fiber length induced by mechanical dissipation. Which theoretical model is correct is still an open question. In this paper, we experimentally investigate the intrinsic thermal noise in optical fibers by using a balanced fiber Michelson interferometer with heterodyne detection technique. When a fiber-stabilized laser with ultralow frequency noise is used as a laser source and other noise sources are carefully controlled, the 1/ fspectral intrinsic thermal noise can be observed down to infrasonic frequency. According to these measurements, in order to verify which theoretical model is the mechanism of generating the intrinsic thermal noise with 1/ fspectral density, we study the relationship between the level of the intrinsic thermal noise and the concentration of the dopant in fibers and the applied tension of fibers. We observe that the level of the 1/ fspectral intrinsic thermal noise is independent of the concentration of the dopant in fibers. This means that the thermoconductive noise model is not suitable to this case. We also observe that the level of the 1/ fspectral intrinsic thermal noise can be reduced by increasing the tension exerted on the optical fibers. Because the mechanical loss of a fiber can be lower than the loss of the material which the fiber is made of when the fiber is subjected to a certain tension, this observation proves the fact that the 1/ fspectral intrinsic thermal noise in optical fibers originates from the mechanical dissipation process inside optical fibers. This is consistent with the predictions of the thermomechanical noise model. Finally, the inconsistency between the experimental data and the theoretical results for thermomechanical noise is discussed.