Mr Mijlof told Sky News the clouds started forming over Table Mountain - about five miles from the city - at around 3pm and his picture was taken three hours later as the formation peaked.
He added: "Honestly, the whole skyline that day was unbelievable and a bit of an eerie stillness in the air.
"I was on my scooter at the time, driving along Signal Hill back home to Camps Bay, I stopped to get this quick shot - I still had my helmet on."
Mr Mijlof said he has seen similar clouds during his travels elsewhere in the world but not in Cape Town.
Sky News meteorologist Chris England said: "They are formed at the top of waves in the atmosphere caused by air going over mountains and are quite common, although more often as long bands of simple arcs."
He said the shapes are formed by either variations in humidity within the air or the originating hills being "fairly isolated peaks".
Picturesque Cape Town is framed by peaks, including Table Mountain, which is around 3,500ft high.
England added: "Lenticular clouds don't really signify anything in particular about the weather, apart from fact that the atmosphere is stable at the time and so not much convection likely - and that can change quite rapidly."
Lenticular clouds, which come from a Latin word meaning "lens-like", can form in many places around the world and have been blamed for a number of previous "UFO sightings".