Maybe, if Starship gets a cargo bay robotic arm. Hubble is 43.5 feet long and 14 feet in diameter and has a mass of 12,000kg, per NASA; that is smaller than the reported volume on Starship, but without a manipulator and an airlock, it would be risky to have people grabbing that mass to wrestle it into the cargo bay without a place to stand.
So far, Starship has had a terrible record and it's not clear that SpaceX will get to the point with Starship that such a mission will ever be possible. They are doing well enough with their Falcon series they may just stick with that.