I want to preface this by saying that the geometry determines the hybridization, not the other way around.
That said, the molecule is not anti-aromatic. For that, the molecule would need to be cyclic, have a conjugated π-electron system, be planar, and have 4n π-electrons within the system. The cycloheptadienyl anion does not meet the 4n π-electron requirement (it has 6 π-electrons, four in the double bonds and two more from the lone pair), and neither does it meet the conjugation or planarity requirements.
In this case, the lone pair does not contribute to making the molecule planar like it would with something like the cyclopentadienyl anion. The carbon with the negative charge on it will be somewhere between $\text{sp}^3$ and $\text{sp}^2$ hybridized. What carbon the anion is on is inconsequential here; a pure $\text{sp}^2$ hybrid is not possible because of the significant ring strain that would develop with this geometry. Regardless, there are always two other tetrahedral carbons (in their $\text{sp}^3$ hybridized geometry) which make the molecule non-planar. You would classify this molecule as non-aromatic.
Cycloheptatrienyl is the more common example, and perhaps what you meant in your question considering you mention 8 π-electrons. Consider (in the photo below) the carbanion; if this molecule was planar, it would be anti-aromatic (4n π-electrons, conjugated, and cyclic) and consequently incredibly unstable. The 'why' behind the instability of this anti-aromaticity (for pretty much all molecules) has to do with the molecular orbitals (which I encourage you to investigate more about). For a shortcut, you can try drawing the Frost circle for the cycloheptatrienyl anion and find the presence two unpaired electrons both in the antibonding MOs! Not very stable.
As pointed out by Mithoron, practically the molecule will bend out of planarity to create a tetrahedral carbon (with the anion on it) to avoid the anti-aromatic destabilization, facilitated by the large enough ring system, making it non-aromatic too.