No, although it will contain solutions.....
The largest proportion of tomato juice is water, which accounts for over 95% of the composition. It will also contain some naturally occurring sugars and proteins, which will be dissolved in the water thereby forming a solution. But tomato juice also contains things like fibre (basically cellulose from plant cell walls) which does not dissolve in water. Therefore tomato juice is basically a dispersion where the continuous phase is a solution.