We present MeerKAT Fornax Survey atomic hydrogen (H I) observations of the dwarf galaxies located in the central ∼2.5 × 4 deg 2 of the Fornax galaxy cluster ( Rvir ∼2°). The H I images presented in this work have a 3 σ column density sensitivity between 2.7 and 50 × 10 18 cm −2 over 25 km s −1 for spatial resolution between 4 and 1 kpc. We are able to detect an impressive MHI = 5 × 10 5M⊙ 3 σ point source with a line width of 50 km s −1 at a distance of 20 Mpc. We detected H I in 17 out of the 304 dwarfs in our field, with 14 out of the 36 late-type dwarfs (LTDs) and three out of the 268 early-type dwarfs (ETDs). The H I-detected LTDs have likely just joined the cluster and are on their first infall as they are located at large clustocentric radii, with comparable MHI and mean stellar surface brightness at fixed luminosity as blue, star-forming LTDs in the field. By contrast, the H I-detected ETDs have likely been in the cluster longer than the LTDs and acquired their H I through a recent merger or accretion from nearby H I. Eight of the H I-detected LTDs host irregular or asymmetric H I emission and disturbed or lopsided stellar emission. There are two clear cases of ram pressure shaping the H I, with the LTDs displaying compressed H I on the side closest to the cluster centre and a one-sided, starless tail pointing away from the cluster centre. The H I-detected dwarfs avoid the most massive potentials (i.e. cluster centre and massive galaxies), consistent with massive galaxies playing an active role in the removal of H I. We created a simple toy model to quantify the timescale of H I stripping in the cluster by reproducing the observed Mr′ - MHI relation. We find that a MHI = 10 8M⊙ dwarf is stripped in ∼240 Myr. The model is consistent with our observations, where low-mass LTDs are directly stripped of their H I from a single encounter and more massive LTDs can harbour a disturbed H I morphology due to longer times or multiple encounters being required to fully strip their H I. This is the first time dwarf galaxies with MHI ≲ 1 × 10 6M⊙ have been detected and resolved beyond the local group and in a galaxy cluster.