The paraglider drifted overhead, said two witnesses who were driving along the ring road around the enclave.
They alerted police at 6.15pm, the Spanish government's representative in Melilla said.
"Patrols immediately headed to the area but were unable to locate the migrant," the representative said.
Footage obtained by local newspaper El Faro shows a person harnessed to a paragliding canopy landing near the road that runs along two parallel border fences, which range between six and 10 metres tall and are 12km long.
The video's authenticity was not verified.
Migrants cross from Morocco to the Spanish enclave of Melilla - in pictures
Melilla is one of the main entry points for migrants seeking to cross into European territory from Morocco.
At least 1,155 undocumented migrants have crossed the land border this year until October 15, according to Interior Ministry data.
It was the site of a fatal mass crossing attempt in June, when up to 2,000 migrants stormed the fence and engaged in a two-hour skirmish with border officers.