We analyze X-ray light curves of the blazar Mrk 421 obtained from the Soft X-ray Imaging Telescope and the Large Area X-Ray Proportional Counter instrument onboard the Indian space telescope $AstroSat$ and archival observations from $Swift$. We show that the X-ray power spectral density (PSD) is a piece-wise power-law with a break, i.e., the index becomes more negative below a characteristic break-timescale. Galactic black hole X-ray binaries and Seyfert galaxies exhibit a similar characteristic timescale in their X-ray variability that is proportional to their respective black hole mass. X-rays in these objects are produced in the accretion disk or corona. Hence, such a timescale is believed to be linked to the properties of the accretion flow. Any relation observed between events in the accretion disk and those in the jet can be used to characterize the disk-jet connection. However, evidence of such link have been scarce and indirect. Mrk 421 is a BL Lac object which has a prominent jet pointed towards us and a weak disk emission, and it is assumed that most of its X-rays are generated in the jet. Hence, existence of the break in its X-ray PSD may indicate that changes in the accretion disk, which may be the source of the break timescale are translating into the jet, where the X-rays are produced.