Mylan NV, whose price increases on its lifesaving EpiPen drug drew broad criticism this month, said Monday it would launch a half-priced generic version of the medicine—in effect, competing against itself.

Mylan said it would begin selling the generic product within weeks for a price of $300 for two injection pens, compared with a list price of about $609 for its branded EpiPen product. The generic version, which delivers the same drug, is expected to eat into Mylan’s revenue from the EpiPen, which had $1 billion in world-wide...