Stocks and the rupiah plunged this month after signs that Widodo, known by his nickname Jokowi, is set to face stiff opposition in parliament that could hamper his ability to enact much-needed reforms in Southeast Asia's biggest economy.
Heavy falls on the market and in the currency last year prompted Bank Indonesia, the central bank, to make a series of aggressive rate hikes.
However the bank left its key rate unchanged at 7.50 per cent Tuesday, where it has been since November last year, with analysts saying policymakers are waiting to see how Widodo will manage the economy after his October 20 inauguration.
Nevertheless, the bank said it remained vigilant to risks on the horizon, including the new leader's plan to hike fuel prices, which would push up inflation. A fast rise in prices could prompt monetary tightening.
"Bank Indonesia will closely monitor various inflation risks, especially the possibility of a subsidised fuel price adjustment," said bank spokesman Tirta Segara.
Fuel subsidies currently take up a huge chunk of the state budget, diverting money away from other crucial programmes, and cutting them is a priority for Widodo.
The bank also estimated that economic growth this year will come in towards the lower end of its forecast of between 5.1 to 5.5 per cent.