The two main sources of the magnetic field in the Martian ionosphere are the solar wind interaction with the planet, and, mainly in the southern hemisphere, remnant crustal magnetization. The magnetic fields measured by the Mars Atmosphere and Volatile EvolutioN (MAVEN) and Mars Global Surveyor spacecraft displayed a wide range of spatial scales, from the global (i.e., L ≈ 103 km) to mesoscale (L ≈ 102 km) to small‐scale (L < 10 km). Hamil et al. (2022) used MAVEN magnetometer and Langmuir Probe data to study these structures and suggested that they might be advected into the ionosphere from the solar wind and magnetosheath. In the current study, we apply a Fourier analysis to the fields and interpret the resulting power spectral density profiles versus frequency. The power spectral density function found from MAVEN data resembles that of the solar wind magnetic field (or interplanetary magnetic field) (i.e., power law with an index of about −2), but shifted upward in frequency by a factor of about 100. From a comparison of ionospheric power spectra with solar wind power spectra, we deduce that plasma, carrying a magnetic field with it moves from the magnetic pile‐up region downward into the ionosphere with speeds of roughly tens of meters per second. The derived power spectra in the ionosphere, in addition to the basic power law shape, show hints of extra power at a spatial scale of about 10 km, and this might be due to the creation of a magnetic structure within the ionosphere itself. Plain Language Summary The two main sources of magnetic field for the Martian ionosphere are the solar wind magnetic fields (i.e., the interplanetary magnetic field), and, particularly in the southern hemisphere, remnant crustal magnetization. The magnetic fields measured in the ionosphere by the magnetometers onboard the Mars Atmosphere and Volatile EvolutioN spacecraft and the Mars Global Surveyor display a wide range of spatial scales. In this study, we use a Fourier analysis of the magnetic field to quantify the field strength as a function of scale‐size. The fourier analysis represents a function of time (or some other variable) as the sum over a wide range of sinusoidal functions of different frequencies. We find that the results of the Fourier analysis for the ionospheric magnetic field have much in common with the Fourier analysis of the interplanetary magnetic field. The study exploits this similarity to probe the sources of the ionosphere's magnetic structure. Key Points A wide range of spatial scales of magnetic structure has been observed in the dayside ionosphere by the Mars Atmosphere and Volatile EvolutioN magnetometer A Fourier analysis of the ionospheric magnetic structure suggests that the power spectrum is like that of the interplanetary magnetic field Simple magnetohydrodynamical theory shows that plasma in the Martian dayside ionosphere flows downward with speeds of tens of meters per second