The Korean won last fell 0.74% to trade at 1,229.59 per dollar. Earlier in the day, it fell as low as 1,241.15 against the greenback on conflicting reports that Kim was unwell.
The South Korean markets also saw declines, with the Kospi closing 1% lower on the day, while the Kosdaq index ended the day 1.42% lower. Shares of defense firm Victek skyrocketed 23.76% while North Korea exposed stocks Hanil Hyundai Cement and Hyundai Elevator dropped 2.48% and 4.7%, respectively.
The moves came after CNN reported Tuesday, citing an unnamed U.S. official with direct knowledge, that Washington was "monitoring intelligence" that Kim is in "grave danger after a surgery."
The North Korean leader was reportedly absent during a celebration of his grandfather's birthday on April 15, raising questions over his health. CNN reported that he had been seen four days prior to that, at a government meeting.
Still, confusion remained over the state of Kim's health.
"We confirm that Chairman Kim Jong Un is currently touring provincial areas with his close aides and we do not detect evidences to support speculation about his ill health," South Korea's presidential office told NBC News.
"Even North Korea's Worker's Party, military or cabinet are showing any special movements such as emergency decree. We believe that Chairman Kim is active as normal as he has been," the office said.
Reuters also reported, citing two government sources, that Kim was not gravely ill.
An earlier report from Reuters had cited a South Korean media website, Daily NK, as saying that Kim was receiving treatment after undergoing a cardiovascular procedure on April 12. That report quoted unidentified sources inside the reclusive regime.
The uncertainty of the situation and "what a potentially new regime might look like" is weighing on markets, Bank of America Securities' Adarsh Sinha told CNBC's "Street Signs" on Tuesday.
"The first thing the (foreign exchange) market does is price in higher risk premium, which means a weaker currency, or a weaker Korean won," said Sinha, who is co-head of Asia rates and foreign exchange strategy at Bank of America Securities.
Many other currencies in Asia also weakened, he added. The onshore Chinese yuan slipped 0.13% to 7.0814 per dollar while its offshore counterpart traded at 7.0955 per dollar. The Singapore dollar also declined 0.3% to 1.4251 against the greenback.
"For the (foreign exchange) market, it's sort of act first and think about the details later," Sinha said.