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We aim at characterizing the low-mass (sub)stellar population of the centralportion (2.4 pc$^2$) of the $\sim$2 Myr old cluster NGC 2244 using nearinfrared spectroscopy. By studying this cluster, characterized by a low stellardensity and numerous OB stars, we aim at exploring the effect that OB stars mayhave on the production of BDs. We obtain near infrared HK spectroscopy of 85faint candidate members of NGC 2244. We derive the spectral type and extinctionby comparison with spectral templates. We evaluate cluster membership usingthree gravity-sensitive spectral indices based on the shape of the $H$-band.Furthermore, we evaluate the infrared excess from Spitzer of all the candidatemembers of the cluster. Finally, we estimate the mass of all the candidatemembers of the cluster and derive the initial mass function, star-to-BD numberratio and disk fraction. The initial mass function is well represented by apower law ($dN/dM \propto M^{-\alpha}$) below 0.4 $M_\odot$, with a slope$\alpha$ = 0.7-1.1 depending on the fitted mass range. We calculate astar-to-BD number ratio of 2.2-2.8. We find the low-mass population of NGC 2244to be consistent with nearby star-forming regions, although it is at thehigh-end of BD production. We find BDs in NGC 2244 to be on average closer toOB stars than to low-mass stars, which could potentially be the first evidenceof OB stars affecting the formation of BDs. We find a disk fraction of all themembers with spectral type later than K0 of 39$\pm$9% which is lower thantypical values found in nearby star-forming regions of similar ages.

Spectroscopic substellar initial mass function of NGC 2244