Widodo discussed plans to establish the fund with Abu Dhabi's Crown Prince Sheikh Mohammed Bin Zayed over the weekend during an official visit there.
Sovereign wealth funds are typically used by countries to direct funds from resource wealth such as oil, although Indonesia also plans to invite foreign investment into its fund.
"When the law presiding over this is issued, we'll have a minimum $20 billion inflow," Widodo told a financial industry event in Jakarta.
Widodo, who began his second term in office in October, is keen for an increase in foreign investment to help create jobs and boost economic growth, which has been stuck at around 5% for several years.
Discussions with the crown prince had included using the sovereign wealth fund to channel investment into the development of Indonesia's new capital city on Borneo island, according to Indonesia's Coordinating Minister for Maritime Affairs and Investment Luhut Pandjaitan.
In an interview with Reuters on Jan. 8, Pandjaitan said the crown prince had agreed in principle to put money into the fund but needed Indonesia to pass a law to ensure legal certainty and then Jakarta would also put in cash and "brownfield" assets.
"When it's been established, anybody can join," said Pandjaitan, adding that the fund would be like an equity fund.
The minister said tech conglomerate Softbank Group Corp and newly established development financier the U.S. International Development Finance Corporation (IDFC) had also expressed interest in investing.
With low-lying Jakarta on Java island facing a range of pressures from congestion to flooding and pollution, President Widodo announced last August a plan to relocate government departments to a site in East Kalimantan on Borneo island.
To help attract investment, Indonesia has asked Abu Dhabi's crown prince, former British Prime Minister Tony Blair and Masayoshi Son, the founder of Softbank, to join a steering committee advising on the $33 billion plan to move the capital, ministers have said.
"Their role on the steering board is to oversee the development of the new capital," Indonesia's chief economic affairs minister Airlangga Hartarto told Reuters on Wednesday.
Planning minister Suharso Monoarfa said that Softbank was interested in providing self-driving vehicles for the capital.
In June, the self-driving car joint venture of SoftBank and Toyota Motor announced plans to begin operating in Southeast Asia this year.
A representatives for Softbank did not immediately respond to a request for comment, while a spokeswoman for former prime minister Blair declined to comment.
By Maikel Jefriando
