"When a head of state or government is stricken like this, it will cause concern for holders of sterling and sterling assets," said Masafumi Yamamoto, chief currency strategist at Mizuho Securities in Tokyo.
"Coronavirus cases in Japan may not peak for another month, so the markets will think that now it's Japan's turn. A state of emergency is necessary, but this could be yen negative."
The pound fell 0.26% to $1.2242 on Monday in Asia. Against the euro, it fell 0.27% to 88.39 pence.
Johnson was admitted in what Downing Street said was a "precautionary step" because he was showing persistent symptoms of COVID-19 10 days after testing positive for the novel coronavirus.
Also weighing on sterling is Britain's constitution - an unwieldy collection of sometimes ancient and contradictory precedents - that offers no formal deputy or caretaker who would take over if Johnson cannot continue to lead.
The coronavirus, which emerged in China late last year, has turned into a pandemic that has infected more than a million people, killed over 68,000 and paralysed large swathes of the global economy.
In the offshore market, China's yuan held steady at 7.1134 per dollar after the mainland reported 39 new coronavirus cases on Sunday, all but one of them imported, up from the 30 reported a day earlier. China's mainland markets are closed Monday for a public holiday.
The yen fell 0.4% to 108.93 against the dollar. It also weakened against the euro, the Australian dollar , and the New Zealand dollar .
Japan's prime minister will declare a state of emergency over the coronavirus as early as Tuesday, the Yomiuri newspaper reported, as the number of infections topped 1,000 in the capital, Tokyo.
Abe will likely announce his plans to declare the emergency on Monday, the paper said.
Pressure has been mounting on the government to make the move as the pace of infections - while slow versus harder-hit countries around the world - continues to accelerate.
The dollar eased slightly to $1.0814 per euro and held steady at 0.9769 Swiss franc.
U.S. President Donald Trump on Sunday expressed hope that the United States was seeing a "leveling-off" of the virus crisis in some of the nation's hot spots.
However, sentiment for the greenback remains fragile after a series of data last week showed U.S. job losses are soaring as draconian measures to curb the virus hurt consumer spending and factory activity.
Currencies of major oil producers fell in Asia on Monday as crude prices gave up some of their recent gains after Saudi Arabia and Russia postponed to Thursday a meeting about a potential pact to cut production.
The rouble lost about 1% against the dollar, while the Mexican peso fell 1.6%. The Norwegian crown NOK= also fell more than 0.3% against the dollar.
(Reporting by Stanley White; editing by Richard Pullin and Himani Sarkar) ((email@example.com; +81 (0)3 4563 2799; twitter.com/stanleywhite1 ;))