Bitcoin’s value passed a record $11,000 (£8,200) on Wednesday after a sharp but often volatile rise this year.
Sir Jon Cunliffe, the Bank’s deputy for financial stability, said that when prices grow so fast, “investors should do their homework and think carefully”.
But he added that Bitcoin’s rise was not big enough to unsettle the economy.
Unlike traditional currencies, Bitcoin is not issued by a central bank or government.
Bitcoin hit a high of $11,377 on one major exchange on Wednesday, an increase of more than 1,000% from the start of the year.