The gap with the official rate, which stood at 37,686 on Monday, has continued to widen. Iran's government took drastic measures last month to stem the decline in the free market rate, arresting foreign exchange dealers, freezing speculators' accounts and raising interest rates, as well as buying up millions of dollars in a bid to lower the price.
But on the streets of Tehran, long queues continued to gather outside foreign exchanges in the build-up to the Nowruz New Year holiday, which is running for another week.
"The issue is psychological rather than economic. There's no reason to buy dollars except in the hope that you can sell them later at a higher rate," said Esfandyar Batmanghelidj, founder of the Europe-Iran Forum, a business network.
He said Iranians were reacting to worrying headlines from the United States, where President Donald Trump recently appointed two hardline anti-Iran figures to his administration: Mike Pompeo as secretary of state and John Bolton as national security advisor.
Many analysts believe Trump will pull out of the 2015 nuclear deal with Iran when it next comes up for renewal in May, bringing back crippling sanctions.
"I see many people looking to invest in neighbouring countries because this fear is spreading about the future of the JCPOA (nuclear deal)," said Navid Kalhor, a Tehran-based financial analyst.
Local officials have complained that Iranians are hoarding billions of dollars, while local banks run short of cash "I have friends who go to banks and ask for 15 or 20 million rials ($300 or $400) and they're told to come back in a week because they're out of cash," said Kalhor.
The devaluation poses a major problem for President Hassan Rouhani's government, which had hoped to attract massive foreign investment in the wake of the nuclear deal.
Already facing huge obstacles from remaining, non-nuclear US sanctions, the collapsing currency will serve as another deterrent to potential investors, said Batmanghelidj.
"Even in an instance where an investor is willing to operate in Iran, the devaluation is very concerning. If you invest now and the currency falls even 15 percent, you have to discount that from your returns, and that's very difficult to hedge against," he said.
"This will be difficult for the government. There is very little they can do about the mentality of individuals."