It depends on your definition of modern. Certainly, this has been a trope at play in Western Literature for a very long time. Obviously, everyone knows about the more famous cases in Western Literature, Viktor Frankenstein being one of the most famous cases. But while Mary Shelly certainly popularized the archetype, she definitely didn't invent it. We also have both Marlowe and Goethe's Faust as another archetypical example of this trope. Even as early as the 17th Century it was already something of a proverb.

"Great wits are sure to madness near allied, and thin partitions do their bounds divide," says the English Poet John Dryden in Absalom and Achitophel in 1681.

But the idea of a link between genius and madness goes back even further, at least back to the early Roman Empire where Seneca allegedly quotes Aristotle.

"No great genius has ever existed without some touch of madness," says Seneca in his Tranquility of the Mind.

Aristotle himself links the two in his Poetics, though the link he holds is far more distant "Poetry demands a man with a special gift for it, or else one with a touch of madness in him.”

So the idea that genius and madness are linked definitely predates the existence of modern medicine. The idea of genius being mad seems to have distinctive Aristotilean undertones, approaching his idea of the Golden Mean. Hume points out his Enquiry Concerning Human Understanding that our cultural idea of a sane person lies somewhere between the highly social idiot and the isolated genius.

"On the other hand, the mere ignorant is still more despised; nor is anything deemed a surer sign of an illiberal genius in an age and nation where the sciences flourish than to be entirely destitute of all relish for those noble entertainments. The most perfect character is supposed to lie between those extremes; retaining an equal ability and taste for books, company, and business; preserving in conversation that discernment and delicacy which arise from polite letters; and in business, that probity and accuracy which are the natural result of a just philosophy."

Does the idea predate Aristotle? There are indications but nothing conclusive. As to the mythological examples... well there are a few shaky ones. Ovid's Metamorphosis mentions the story of the famous inventor Daedalus who kills his own nephew, Perdix, in a fit of envy, though whether this constitutes madness or just sheer malice is up to interpretation. The Völundarkvitha poem from the Poetic Edda mentions some truly dark acts of revenge by the brilliant smith Wayland (or Volund, in the poem), but again, whether this is an example of a 'Mad Genius' is up for interpretation.

So to summarize the first part of the question, it is a very old trope in Western culture. As to whether it's prevalent in nonwestern culture, I'd have to defer to someone with more expertise in that area.