In a statement, the Monetary Authority of Singapore (MAS) said it had also asked state prosecutors to investigate six senior executives of BSI Bank Limited, including its former chief executive, for possible criminal offences.
In the toughest legal action so far in the crisis rocking Malaysian state fund 1MDB, Switzerland also disclosed it had launched criminal proceedings against the parent firm BSI SA for "deficiencies" in its internal organization.
Two Singaporean executives of the bank are already facing charges in the city-state, which is Southeast Asia's financial hub.
The MAS said it has served BSI Bank with a "notice of intention to withdraw its status as a merchant bank in Singapore for serious breaches of anti-money laundering requirements, poor management oversight of the bank's operations, and gross misconduct by some of the bank's staff".
It is the first time the MAS has cancelled the licence of a merchant bank since 1984, when the local branch of Jardine Fleming was shut down for "serious lapses" in its advisory work, the statement said.
1MDB, founded in 2009 by Najib, is teetering on the brink of collapse amid multiple investigations around the world into allegations that billions were looted from it.
The fund, which ran up more than $11 billion in debt in a series of much-questioned investments, has steadfastly denied money was stolen or that it was in financial trouble.
Najib was plunged into the crisis last year when the Wall Street Journal revealed $681 million in transfers to his personal bank accounts.
He claims the money was a gift from the Saudi royal family, most of which he returned. A Saudi official in April said that was true, but only after weeks of silence that cast doubt on the claim.
In a series of more recent investigative reports, however, the newspaper said Malaysian investigation documents indicated more than $1 billion in 1MDB-linked money had been funnelled to Najib.
Najib and 1MDB vehemently deny that claim.
Najib has faced calls to resign but he has tightened his grip on the ruling party and thwarted domestic investigations. His position is not seen as under imminent threat.