Foreign banks are not allowed to operate in Myanmar and the local banking system is rudimentary, so the interbank market is likely to be tiny initially.
"We have allowed local private banks to trade in foreign currency among themselves effective today, taking a major step forward in financial reforms," the central bank official told Reuters.
"They now can compete on equal terms with each other with compete transparency," he added, asking for anonymity since he was speaking to the media without authorisation.
Than Lwin, vice-chairman of KBZ Bank, the biggest private lender in the country, and a retired vice-governor of the central bank, said: "We do welcome their allowing interbank marketing. It's a big step towards the emergence of a foreign exchange market."
President Thein Sein took office in March 2011 and, at the head of a quasi-civilian government, has opened up Myanmar with a series of political and economic reforms, after half a century of military rule.
Under International Monetary Fund supervision, the authorities started unifying the various exchange rates at the time of the introduction of the managed float in 2012, and the central bank started selling foreign currency to private banks through auctions.
In an annual report on Myanmar's economy published late on Friday, the IMF said that as of May the currency had fallen about 13.5 percent since the float, which had taken it closer to its long-run fundamental value. Last year it said the kyat was as much as 40 percent overvalued.
The central bank sets a benchmark rate against the dollar each day. On Monday, it was 975 kyat per dollar, down from 945 on May 31, central bank data showed.
The president enacted a law in July that gave the central bank greater independence. Previously, it was part of the Ministry of Finance.