This would have some amount of effect on the earth, though I'm not knowledgeable enough to say what the effect would be. I could imagine the result being anywhere from "it's measurable with scientific instruments" and up to "all life on earth will die within hours".

~~Off the top of my head iirc Neptune prevents a huge amount of large meteors from hitting the earth, so i think for that reason alone it would lead to earth being frequently hit with meteors that each cause nuclear weapon level of destruction.~~

EDIT

Actually Jupiter is the planet that protects us from asteroids, so that specific effect probably wouldn't be in play