Differences of opinion with the Asia-Pacific Breweries' regional Tiger Beer team is believed to have prompted the decision.
BBH scooped the business in December from BBDO following a six-month pitch process.
John Hadfield, BBH's Asia-Pacific managing director, said: "We had a very compelling proposition for Tiger, and still enjoy a great relationship with the local team, so it is particularly frustrating that we will not be able to bring this to fruition."
He added: "Initial feedback from the client was very positive, and it would have been a privilege to work on what is an iconic Singapore brand."