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We present the first measurement of the H  i mass function (HIMF) using data from MeerKAT, based on 276 direct detections from the MeerKAT International GigaHertz Tiered Extragalactic Exploration (MIGHTEE) Survey Early Science data covering a period of approximately a billion years (0 ≤ |$z$| ≤ 0.084). This is the first HIMF measured using interferometric data over non-group or cluster field, i.e. a deep blank field. We constrain the parameters of the Schechter function that describes the HIMF with two different methods: |$1/V_{\rm max}$| and modified maximum likelihood (MML). We find a low-mass slope |$\alpha =-1.29^{+0.37}_{-0.26}$| , 'knee' mass |$\log _{10}(M_{*}/{\rm {\rm M}_{\odot }}) = 10.07^{+0.24}_{-0.24}$| and normalization |$\log _{10}(\phi _{*}/\rm Mpc^{-3})=-2.34^{+0.32}_{-0.36}$| (H 0 = 67.4 km s−1 Mpc−1) for |$1/V_{\rm max}$| , and |$\alpha =-1.44^{+0.13}_{-0.10}$| , 'knee' mass |$\log _{10}(M_{*}/{\rm {\rm M}_{\odot }}) = 10.22^{+0.10}_{-0.13}$| and normalization |$\log _{10}(\phi _{*}/\rm Mpc^{-3})=-2.52^{+0.19}_{-0.14}$| for MML. When using |$1/V_{\rm max}$| we find both the low-mass slope and 'knee' mass to be consistent within 1σ with previous studies based on single-dish surveys. The cosmological mass density of H  i is found to be slightly larger than previously reported: |$\Omega _{\rm H\,{\small I}}=5.46^{+0.94}_{-0.99} \times 10^{-4}\,h^{-1}_{67.4}$| from |$1/V_{\rm max}$| and |$\Omega _{\rm H\,{\small I}}=6.31^{+0.31}_{-0.31} \times 10^{-4}\,h^{-1}_{67.4}$| from MML but consistent within the uncertainties. We find no evidence for evolution of the HIMF over the last billion years. [ABSTRACT FROM AUTHOR]