Kweku Adoboli, believed to work in the European equities division, was detained in the early hours of Thursday and remains in custody.
UBS shares fell 8% after it announced it was investigating rogue trades.
The Swiss bank said no customer accounts were affected.
A spokesman for City of London Police, which is responsible for the city’s financial district, said: “We can confirm we arrested a 31-year-old man at 3:30am on suspicion of fraud by abuse of position.”
In a letter to its 65,000 staff, UBS warned that the rogue trades could hit profits.
“The matter is still being investigated, but UBS’s current estimate of the loss on the trades is in the range of $2bn,” the bank said.
“It is possible that this could lead UBS to report a loss for the third quarter of 2011. No client positions were affected.
“While the news is distressing, it will not change the fundamental strength of our firm.
“We urge you to stay focused on your clients, who are counting on you to guide them through these uncertain times,” the bank said.
“Start Quote All the clever systems that the banks now have still cannot stop a determined individual ” Chris Roebuck.
Visiting professor, Cass Business School The Financial Times newspaper reported that Mr Adoboli worked as a director of Exchange Traded Funds in the equities department.
ETF’s are a type of tradeable share that track movements in other indexes or commodities, and can be affected by short-term volatility in prices.
ZKB trading analyst Claude Zehnder said the news would damage confidence in UBS. “They obviously have a problem with risk management.
“With this, they are losing a lot of credit that they had regained with effort.”
UBS was rescued by the Swiss state in 2008, following huge losses on toxic assets held by its investment bank.
It then became embroiled in a serious tax evasion dispute with US authorities and was forced to hand over 300 client names and pay a $780m fine. There was then a second case in which it agreed to hand over data on 4,450 American clients.
UBS declined to say in which department, or country, the rogue trader operated. However, there is already speculation that the losses may have occurred in foreign exchange trades.
Earlier this month, the Swiss Central Bank shocked the markets by capping the franc against the euro at 1.20 francs. The move sent the franc-euro exchange rate up 10%, and it is rumoured that some traders lost money.
The UBS news has echoes of other rogue trades, including at Societe Generale, where former trader Jerome Kerviel was arrested in 2008 over unauthorised trades which cost the bank 4.9bn euros.
That topped the losses involved in the infamous case in 1995, which saw Briton Nick Leeson cause the collapse of Barings bank after costing the group £800m.
Banks such as UBS have tightened their compliance and rules, but this latest breach “is a staggering demonstration that all the clever systems that the banks now have still cannot stop a determined individual getting round them if they want to,” said professor Chris Roebuck.
Mr Roebuck, visiting professor at Cass Business School, said it would fuel the debate over “casino” banking.
“We will see how the good shareholders of UBS react to yet another investment banking debacle as they ponder their mountain views, probably wishing that the investment bank was caught in the next avalanche and swept away,” he said.
The UBS announcement came on the day that the lower house of the Swiss parliament was due to discuss the country’s banking laws to reduce the risks from firms that are considered “too big to fail”.
Last month the bank announced 3,500 jobs cuts. Of the 65,000 staff worldwide about 6,000 are in the UK, with the bulk of UBS’s investment banking operations based in London and New York.