Tear gas was used to disperse the demonstrators, some of whom were setting fire to tyres and rubbish bins. There were many arrests, reports say.
Eyewitnesses told the BBC that scores of people gathered outside the central bank, calling for the governor to stand down, chanting anti-government slogans.
The rial has plummeted to record lows against the US dollar in recent days.
Up to 100 angry traders and official money lenders gathered in front of Iran's central bank. But they were attacked by riot police and dispersed, eyewitnesses told BBC Persian.
Reports say many shops in the central Grand Bazaar have brought down their shutters in sympathy with the demonstrators.
Traders are angry at the lack of direction from the government in the crisis, which they say has led to more instability in prices, making trading almost impossible, says BBC Persian's Kasra Naji.
The head of Tehran's bazaar unions, Ahmad Karimi-Esfahani, said shopkeepers had not opened their businesses as they were "worried about their security" but he expected them to reopen on Thursday.
He said a protest outside the bazaar started with a small group and then grew, he told the Iranian Labour News Agency (Ilna).
A senior Iranian police commander confirmed to Ilna that "a limited number of people protested in front of the bazaar," but he said the bazaar was not closed.
Hundreds of police are also reported to have rounded up and arrested illegal money changers in the capital.
Iranian President Mahmoud Ahmadinejad has blamed Western sanctions for the fall in the rial, saying they amounted to an economic war.
However, many Iranians accuse him of financial mismanagement.
US officials say the slide reflects the success of US economic sanctions targeted at Iran's controversial nuclear programme.
In a separate development, the speaker of parliament, Ali Larijani, who was due to give a news conference has cancelled it without explanation.
He was expected to respond to President Ahmadinejad's accusation that he had undermined the government and lacked ideas on how to deal with the crisis.