There seems to be several reasons for this, all inter-related.
First, throughout history, Jewish people have, on average, been wealthier than non-Jewish people. The most obvious and likely explanation is that the Jewish culture traditionally emphasizes education and hard work.
From a book about networks:
We are compelled by the data [which demonstrates Jewish success] to fallback on more intangible explanations, such as genetics, or the educational benefits of Jewish family life, or some kind of Weberian “Jewish ethic” even more aligned with the spirit of capitalism than the Protestant ethic.
(Note: I don’t understand the reference to genetics there. That seems incongruous with the rest of the passage.)
But there are other, more sinister theories.
In the Middle Ages, Jews often worked in finance. Christian dogma at the time prevented Christians from loaning money to each other with interest. To get around this, a Christian would loan money to a Jewish middleman, with interest, who would then loan it to the intended Christian recipient, again with interest.
(This rule does not seem to be strictly Biblical. It was announced at the Third Laterean Council in 1179, and reaffirmed at the Council of Vienna in 1311.)
(Also, technically Jews couldn’t lend to other Jews with interest either. But conveniently, the mechanics of the transaction meant that no two people of the same belief where directly engaged with one another.)
This was an end run around religious law, and the side effect was that it put a Jew in the middle of a transaction in which they passively made money. This often caused resentment from Christians (even though it was their beliefs that required it), and moneylending became something Jews were associated with.
Consider the Shakespearean play The Merchant of Venice, written in the late 1500s. The entire plot revolves around a Jewish moneylender named Shylock – a name which itself has become a racial slur – who loans money to a Catholic merchant, and requires its repayment or a gruesome alternative, involving “a pound of flesh.”
Finally, Jewish society tended to be segregated due to escalating prejudice (see Borscht Belt). They were physically segregated in areas of a city called “ghettos,” and consequently, Jewish culture became naturally insular. This, combined with their general success in business and association with finance, resulted in jealousy and fears that Jews were quietly conspiring to hoard wealth.
A lot of bigotry is based on “sour grapes.” The Jewish people have traditionally been financially successful, which is desirable, so people who are jealous of this seek to justify their relative lack of success by explaining that “Jews are obsessed with money.” (Note that no one ever accuses a racial group of being “obsessed with soup spoons” or something else not inherently desirable.)
In the end, the stereotype has likely persisted because its convenient. Bigots want a reason to hate other groups, and this stereotype is handy.