The "Tehran-e Emrouz" newspaper reports that the company, called the "Ladies' Safe Trips" taxi company, will be the first such private firm in the capital.
Similar taxi companies have been operating in Iranian other cities for several years.
The company will employ only married female drivers.
Under Islamic law in Iran, men and women mostly travel in separate sections on public transport.
But it is common for men and women to share taxis in many cities, often in cramped conditions.