Wavemeters are very important for precise and accurate measurements of both pulses and continuous-wave optical sources. Conventional wavemeters employ gratings, prisms, and other wavelength-sensitive devices in their design. Here, we report a simple and low-cost wavemeter based on a section of multimode fiber (MMF). The concept is to correlate the multimodal interference pattern (i.e., speckle patterns or specklegrams) at the end face of an MMF with the wavelength of the input light source. Through a series of experiments, specklegrams from the end face of an MMF as captured by a CCD camera (acting as a low-cost interrogation unit) were analyzed using a convolutional neural network (CNN) model. The developed machine learning specklegram wavemeter (MaSWave) can accurately map specklegrams of wavelengths up to 1 pm resolution when employing a 0.1 m long MMF. Moreover, the CNN was trained with several categories of image datasets (from 10 nm to 1 pm wavelength shifts). In addition, analysis for different step-index and graded-index MMF types was carried out. The work shows how further robustness to the effects of environmental changes (mainly vibrations and temperature changes) can be achieved at the expense of decreased wavelength shift resolution, by employing a shorter length MMF section (e.g., 0.02 m long MMF). In summary, this work demonstrates how a machine learning model can be used for the analysis of specklegrams in the design of a wavemeter.