England are set to face India in the last four in Sydney at 04:00 GMT.
However, Tropical Storm Esther is expected to bring rain for most of Thursday.
With no reserve day in place for the semi-finals, India will progress if no result is possible as they won Group A whereas England came second in Group B.
Defending champions Australia meet South Africa in the second semi-final at 08:00 GMT and the hosts would face the same fate as England in the event of a no result because they were runners-up in Group A.
“With the rain eventually clearing away later on Thursday, there’s a very small chance of some drier weather for the second semi-final but it may be too late in the day,” King added.
The final takes place on Sunday at the Melbourne Cricket Ground with organisers hoping to set a new attendance record for a women’s sporting event.
England’s 2017 World Cup winner Alex Hartley told Test Match Special it is “mind-blowing” there is no reserve day for the semi-final. The forecast for Sydney on Friday is for sunshine.
“Rain happens, even in Australia,” Hartley said. “I’d rather have the chance of playing – it’s an hour’s flight to Melbourne from Sydney. It’s not like they’re asking players to fly halfway round the world.
“India and South Africa have played the most consistent cricket so they do deserve to be top of the group but it is mind-blowing there’s no reserve day.”
On Tuesday, South Africa’s match against West Indies was washed out, sealing the Proteas’ place as Group B winners and confirming England’s second-place finish.
Thailand’s match against Pakistan was also abandoned with only 20 overs possible.