The decision could stall Turkey's crypto market, which has gained momentum in recent months as investors joined the global rally in bitcoin, seeking to hedge against lira depreciation and inflation that topped 16% last month.
In a statement, the central bank said crypto assets were "neither subject to any regulation and supervision mechanisms nor a central regulatory authority", among other security risks.
BNY Mellon's investment was part of a $133 million funding round that also saw participation from hedge fund Coatue Management, investment firm Ribbit Capital, growth equity firm Stripes and SVB Capital.
Fireblocks has a presence in Europe, Asia and North America, with customers including banks, neobanks, exchanges, hedge funds and market makers.
The terms of the deal, which is expected to complete in the first half of 2021, were not disclosed. Curv would be part of PayPal's recently created cryptocurrencies-focused unit.
PayPal said in October last year, it would allow customers to buy, sell and hold cryptocurrencies in its online wallets.
The world's biggest cryptocurrency slipped as much as 6% to $44,451 before recovering most of its losses.
The sell-off echoed that in equity markets, where European stocks tumbled as much as 1.5%, with concerns over lofty valuations also hammering demand. Asian stocks fell by the most in nine months.