The Geminids meteoroid stream produces one of the most intense meteor showers at Earth. It is an unusual stream in that its parent body is understood to be an asteroid, (3200) Phaethon, unlike most streams, which are formed via ongoing cometary activity. Until recently, our primary understanding of this stream came from Earth-based measurements of the Geminids meteor shower. However, the Parker Solar Probe (PSP) spacecraft has transited near the core of the stream close to its perihelion and provides a new platform to better understand this unique stream. Here, we create a dynamical model of the Geminids meteoroid stream, calibrate its total density to Earth-based measurements, and compare this model to recent observations of the dust environment near the Sun by PSP. For the formation mechanisms considered, we find with the exception of very near perihelion the core of the meteoroid stream predominantly lies interior to the orbit of its parent body and we expect grains in the stream to be ≳10 μm in radius. Data–model comparisons of the location of the stream relative to Phaethon’s orbit near perihelion are more consistent with a catastrophic formation scenario, with the core stream residing near or outside the orbit of its parent body consistent with PSP observations. This is in contrast to a cometary formation mechanism, where even near the Sun the meteoroid stream is interior to the orbit of its parent body. Finally, while PSP transits very near the core of the stream, the impact rate expected from Geminids meteoroids is orders of magnitude below the impact rates observed by PSP, and hence undetectable in situ. We similarly expect the upcoming DESTINY+ mission to be unable to detect appreciable quantities of Geminids grains far from (3200) Phaethon.