Fiber Bragg grating (FBG) sensors have been widely applied for structural health monitoring applications. In some applications, remote bonding of the optical fiber is applied, where ultrasonic waves are coupled from the structure to the optical fiber and propagated along the fiber to the FBG sensor. The distance that this signal can propagate along the optical fiber without decaying below a threshold value can be critical to the area of the structure that can be monitored per sensor. In this paper, we develop a method to measure the acoustic mode attenuation of fiber waveguides based on laser Doppler vibrometry (LDV) that is independent of the fiber type. In order to validate the method, we compare attenuation measurements on single-mode optical fibers using both the LDV and FBG sensor methods. Once the method is validated, experimental measurements of different coated and uncoated optical fibers are performed to quantify the role of the fiber diameter on the attenuation coefficient. As the radius of the waveguide decreases, the signal attenuation increases exponentially.