We present the stellar and substellar mass function (MF) of the open cluster IC 2391, plus its radial dependence, and use this to put constraints on the formation mechanism of brown dwarfs (BDs). Our multi-band optical and infrared photometric survey with spectroscopic follow-up covers 11 deg2, making it the largest survey of this cluster to date. We observe a radial variation in the MF over the range 0.072-0.3 M sun, but no significant variation in the MF below the substellar boundary at the three cluster radius intervals is analyzed. This lack of radial variation for low masses is what we would expect with the ejection scenario for BD formation, although considering that IC 2391 has an age about three times older than its crossing time, we expect that BDs with a velocity greater than the escape velocity have already escaped the cluster. Alternatively, the variation in the MF of the stellar objects could be an indication that they have undergone mass segregation via dynamical evolution. We also observe a significant variation across the cluster in the color of the (background) field star locus in color-magnitude diagrams and conclude that this is due to variable background extinction in the Galactic plane. From our preliminary spectroscopic follow-up, to confirm BD status and cluster membership, we find that all candidates are M dwarfs (in either the field or the cluster), demonstrating the efficiency of our photometric selection method in avoiding contaminants (e.g., red giants). About half of our photometric candidates for which we have spectra are spectroscopically confirmed as cluster members; two are new spectroscopically confirmed BD members of IC 2391.