OTE is 40 percent-owned and managed by Deutsche Telekom , with the state holding a 10 percent stake.
Under its third international aid programme signed last year, Greece has agreed an ambitious privatisation scheme - including the sale of half of its shares in OTE - aiming at raising 14 billion euros ($15 billion) by 2022.
The transfer of the 5 percent shareholding to HRADF was published in the government's official gazette on Friday.
The agency will now need to hire an adviser to proceed with the sale, the precise timing of which is unclear. Deutsche Telekom has a right of first refusal in any sale.
Some opposition lawmakers and OME-OTE, OTE's largest trade union which represents 14,000 workers in the company, oppose a sale, saying Greece will lose its influence in a strategically important company.
OTE, which also operates in Romania and Albania, is Greece's second-biggest listed company with a market value of $4.3 billion. A 5 percent stake could raise 216 million euros for the state based on Friday's stock price.