Dark matter (DM), if captured in considerable amounts at the Solar core may undergo the process of self-annihilation producing standard model particles such as neutrinos, charged leptons, or gamma as the end product. Neutrinos, thus produced in the Solar core from DM annihilation may be detected at a terrestrial neutrino detector. KM3NeT is an under-sea neutrino detector at the Mediterranean sea where the sea water is the detecting material. Neutrinos are detected by the Cherenkov light due to charge leptons obtained from the charge current interaction and/or neutral current scattering of neutrinos with the seawater detector of KM3NeT. In this talk, I will discuss the detectability of such DM neutrinos from the Sun at the upcoming KM3NeT detector. I will present our works related to the computation of upper bounds of muon event rates for different annihilating dark matter masses for each of the cases of dark matter annihilation channels (e.g. $b \bar{b}$ , $W^+W^−$, $Z\bar{Z}$ , etc). These upper bounds of the detection rate for such neutrinos at KM3NeT are computed for the case of a generic dark matter scenario and also when specific models for particle dark matter are chosen.