Space is big.
Really big. You just won't believe how vastly, hugely, mind-boggling big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen; when you're thinking big, think bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real 'wow, that's big', time. It's just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we're trying to get across here.
(Douglas Adams, The Hitchhiker's Guide to the Galaxy)
If you increased the ship size to that of Luna, our beloved moon, and changed the incoming travel vector such that, in the fullness of time, the debris from the impact would exactly collide with Mars — it would cause (at best) a delightful but completely harmless meteor shower.
If (and it's a big if) you hit the planet with enough kinetic energy to shatter the planet...
The planet is in orbit around the sun and most of the mass would continue in that orbit.
The planet is rotating, so the exploding mass is spinning away like a top.
Space has three dimensions and the location of a planet is actually an infinitesimally small point within the massive and voluminous sphere that encloses the solar system. If you actually could cause the planetary mass to eject away such that the planetary orbit didn't matter, the vast, vast, vast, vast, vast majority of mass wouldn't go anywhere near another planet. (That same number of vasts could be said of the amount that wouldn't go anywhere near the Sun....)
So, from the perspective of the blown apart mass being a threat to any other planet in the solar system the answer is no, zilch, nada, niet, ei mitään.
But there would be a small effect
The eventually distribution of planetary mass means that the gravity well represented by Earth is gone. That will effect the other planets to a small degree. They'll slightly change position, but I suspect not by much. Someone with more experience in Celestial Mechanics is needed to say how much. But I doubt it would be catastrophic in any sense of the word.