Water solidity won't prevent it, but other factors will
Water is not a solid unless it freezes. When you fall into water from a high enough altitude it feels solid but it isn't. The phenomena of it "feeling solid" is actually the fact that the object (us) has less binding energy than the kinetic energy upon impact. Therefore, water not being solid would not prevent the Arcane Eye. It being in water could hinder or alter what the eye sees depending on DM ruling on how clear the water is.
Water and the Arcane Eye
The spell Arcane Eye states:
You create an invisible, magical eye within range that hovers in the air for the duration.
Since spells do what they say they do and nothing else, the Arcane Eye would not be hovering nor in the air, so therefore cannot be used underwater.
The solidity of water does not matter in this case. What matters is that the eye would not be able to be used underwater because of the wording of the spell.