Ben Broadbent made the comment when comparing the current slowdown to the lull at the end of the 19th century between the ages of steam and electricity.
In a Telegraph interview, he said some economists used the term “climacteric” to describe that period.
Mr Broadbent said the biological term could apply to both genders but essentially meant “menopausal” and is used for economies that are “past their peak and no longer so potent”.
Mr Broadbent said the cause of the current productivity slowdown, which has lasted almost 10 years, was uncertain but the knock-on effect means there is less money for public spending.
Following some criticism, Mr Broadbent said: “I’m sorry for my poor choice of language… and regret the offence caused.”
He added: “I was explaining the meaning of the word “climacteric”, a term used by economic historians to describe a period of low productivity growth during the nineteenth century. Economic productivity is something which affects every one of us, of all ages and genders.”
Some Twitter users, however, were not impressed with the deputy governor’s choice of words.
@SebCavendish said: “Inappropriate use of the word; for many women menopause is liberating, freedom. Shame on you Bank of England’s Ben Broadbent.”
Another, @amelie_elyse, tweeted: “Mr Broadbent et al. clearly need to grow up and conjure up some less sexist economic jargon.”
And Elizabeth Burke, an investor and lawyer, said: “I guess the man has a very limited vocabulary.”
Mr Broadbent, who sits on the Bank of England’s rate-setting committee, also told the Telegraph the bank would not “spoon feed” markets with interest rate guidance.
“Our communication is mainly addressed to the wider public,” Mr Broadbent told The Telegraph. “Their (the City’s) job is to put themselves in our shoes. We all have the same data.”