Weakly interacting massive particles (WIMPs) can be captured by the Sun and annihilate in the core, which may result in production of kaons that can decay at rest into monoenergetic 236 MeV neutrinos. Several studies of detection of these neutrinos at DUNE have been carried out. It has been shown that if the WIMP mass is below 4 GeV, then they will evaporate prior to annihilation, suppressing the signal. Since Jupiter has a cooler core, WIMPs with masses in the 1–4 GeV range will not evaporate and can thus annihilate into kaons which decay at rest into monoenergetic neutrinos. We calculate the flux of these neutrinos near the surface of Jupiter and find that it is comparable to the flux of neutrinos from the Sun at DUNE for masses above 4 GeV and substantially greater in the 1–4 GeV range. Of course, detecting these neutrinos would require a neutrino detector near Jupiter. Obviously, it will be many decades before such a detector can be built, but should direct detection experiments find a WIMP with a mass in the 1–4 GeV range, it may be one of the few ways to learn about the annihilation process. A liquid hydrogen time projection chamber might be able to get precise directional information and energy of these neutrinos (and hydrogen is plentiful in the vicinity of Jupiter). We speculate that such a detector could be placed on the far side of one of the tidally locked Amalthean moons; the moon itself would provide substantial background shielding and the surface would allow easier deployment of solar panels for power generation.