The Central Bank of Iran (CBI) said that nearly 16.5 million households had received the 10-million-rial ($62.5) payment as of Thursday evening local time, Press TV reported.
It said that the cash would be deposited in the bank accounts of another 500,000 families later in the day.
The CBI said several million more families would be provided with the relief next week.
The payment is part of a series of inclusive measures adopted by the Iranian government to mitigate the economic impacts of the pandemic as many people have temporarily lost their jobs because of the outbreak.
The government has eased some of its lockdown measures which have been in place since early March, allowing some businesses and industries to gradually reopen. However, cash has been offered to many people to compensate for losses suffered during the outbreak.
The inclusive cash handouts, which covers nearly 23 million people, has cost the government around $1.6 billion. Families will return the interest-free loan in 30 months through deductions made from their monthly benefits.
The government has provided other forms of cash support to nearly three million workers directly affected by the pandemic. Another four million people have received loans worth 10-20 million rials.
The Iranian Health Ministry said on Friday that coronavirus has infected 88,194 people in the country, of which nearly 66,596 people have recovered and 5,574 have died.
The outbreak was first noticed in Iran in late February.