Add the strawberries and water to a blender and blend until smooth.
Strain the mixture to remove seeds if desired.
Pour the mixture back into the blender and add sweetened condensed milk, cream, and sugar (if using).
Blend again until everything is well combined and smooth.
Pour into popsicle molds and insert sticks.
Freeze for at least 6 hours or overnight until solid.
To release, run warm water on the outside of the molds for a few seconds.