Comco said it had evidence indicating that UBS, Switzerland's largest bank, and and Zurich-based private bank Julius Bär reached illegal agreements with other banks over the trading of precious metals.
Foreign banks alleged to be involved in the alleged collusion include Deutsche Bank, HSBC, Barclays, Morgan Stanley and MItsui.
They are suspected, in particular, of possible agreements in the fixing of precious metal prices, notably in the “spreads”, the difference between the buying and selling prices, Comco said in a statement.
The precious metals involved include gold, silver, platinum and palladium.
"We think they can have manipulated the price of these precious metals," Comco deputy chief Patric Ducrey told AFP.
Ducrey said the banks had all been informed of the ongoing probe, and that the investigation would likely conclude in 2017.
It is not the first time the role of banks in determining the price of precious metals has been questioned.
In August, the European Commission said it was "currently investigating alleged anti-competitive behaviour in precious metals spot trading in the EEA" (European Economic Area), but provided no further details.
And in February, the US Justice Department reportedly opened its own investigation into possible manipulation of precious metals markets by ten major international banks: HSBC, Bank of Nova Scotia, Barclays, Credit Suisse, Deutsche Bank, Goldman Sachs, JP Morgan, Société Générale, Standard Bank and UBS.
Goldman Sachs, HSBC, Standard Bank of South Africa and the German chemical group BASF have also been under investigation since last November over a complaint alleging rigging of the prices of platinum and palladium.
'We will constructively cooperate'
Julius Bär, which was not part of the US investigation, told AFP on Monday that it was aware of the Swiss probe.
"We will constructively cooperate with this investigation," said spokesman Jan Vonder Muehl.
UBS, which did not immediately return requests for comment on Monday, said in May it had won immunity from criminal fraud charges in the US probe, after agreeing to provide the Justice Department with information about precious metal transactions.
In its second quarter report, Switzerland's largest bank meanwhile said a number of authorities around the world were reportedly "investigating potential manipulation of precious metals prices."
Precious metals have increasingly come under scrutiny after the discovery that other financial benchmarks have been rigged.
Some of the banks under investigation on Monday were already hit by massive fines earlier this year after pleading guilty to US charges of conspiring to rig Libor rates, the global commercial interest rate benchmark used to peg millions of rate-sensitive contracts and loans around the world.
That rate is estimated to underpin some $500 trillion worth of contracts.
The price-setting mechanism to determine benchmark prices for precious metals has also been under reform, amid calls for greater transparency.
Panels of banks have until recently agreed on the reference prices for the precious metals.
But last year, exchange giant CME Group and financial information giant Thomson Reuters began providing an electronic system for setting benchmark silver prices, and the London Metal Exchange (LME) did the same for platinum and palladium.
There are also moves underway to reform the century-old method of gold price "fixing," since the current global benchmark, London's Gold Fix, has already been tainted by a rigging scandal and attacked by critics as old-fashioned.
A new method for setting the gold benchmark price is expected to take effect next March.
Following the news, the two Swiss banks on Comco's list, UBS and Julius Bär, saw their share prices slump 1.16 and 1.08 percent respectively in late morning trading, as the Swiss stock exchange's main SMI index fell just 0.24 percent.