ABUJA, Nigeria—Nigeria’s central bank abandoned a currency peg that economists and businesses had long blamed for exacerbating a slide toward recession in Africa’s largest economy.

Central Bank of Nigeria Gov. Godwin Emefiele said Wednesday that the country’s naira currency will trade at a market-determined rate beginning Monday, rather than the 197-per-U.S.-dollar level the bank has mandated for more than a year.

The...