In the context of whether a massive compact object recently observed in the GW190814 event is a neutron star (NS) or not, we study the role of the parameters κ and Λc of the Eddington-inspired Born-Infeld (EiBI) gravity theory in the NS mass-radius relation, moment of inertia, and tidal deformability. The results are compared to recent observational constraints extracted from the analysis of NS observation data. The NS core equation of state (EoS) is calculated using the relativistic mean-field model with the G3 parameter set. In the hyperon sector, the SU(3) and hyperon potential depths are used to determine the hyperon coupling constants. For the inner and outer crusts, we use the crust EoS from Miyatsu et al. [Astrophys. J. 777, 4 (2013)ASJOAB0004-637X10.1088/0004-637X/777/1/4]. We also maintain the sound speed to not exceed c/3 at high densities. We find that, in general, the NS mass significantly depends on the value of κ, and the radius R is sensitive to the value of Λc. Moreover, as Λc is equal to zero or less than the accepted bound of the cosmological constant, the NS within the EiBI theory is compatible with observational constraints, including 2.0 M mass, canonical radius R1.4 M, moment of inertia, and tidal deformation. Our investigation also reveals that the 2.6 M mass compact object and current observational constraint of canonical radius R1.4 M can simultaneously be satisfied only when the Λc value is unphysically too large and negative. Therefore, within the specific EoS employed in this work, we conclude that the secondary object with 2.6 M observed in the GW190814 event  is not likely a static (or a slow-rotating) NS within the EiBI gravity theory.