Planets of 1-4 times Earth's size on orbits shorter than 100 days exist around 30-50% of all Sun-like stars. These ``hot super-Earths'' (or ``mini-Neptunes''), or their building blocks, might have formed on wider orbits and migrated inward due to interactions with the gaseous protoplanetary disk. The Solar System is statistically unusual in its lack of hot super-Earths. Here, we use a suite of dynamical simulations to show that gas-giant planets act as barriers to the inward migration of super-Earths initially placed on more distant orbits. Jupiter's early formation may have prevented Uranus and Neptune (and perhaps Saturn's core) from becoming hot super-Earths. It may actually have been crucial to the very formation of Uranus and Neptune. In fact, the large spin obliquities of these two planets argue that they experienced a stage of giant impacts from multi-Earth mass planetary embryos. We show that the dynamical barrier offered by Jupiter favors the mutual accretion of multiple migrating planetary embryos, favoring the formation of a few massive objects like Uranus and Neptune. Our model predicts that the populations of hot super-Earth systems and Jupiter-like planets should be anti-correlated: gas giants (especially if they form early) should be rare in systems with many hot super-Earths. Testing this prediction will constitute a crucial assessment of the validity of the migration hypothesis for the origin of close-in super-Earths.