Eureka 10 Day Weather. 1  Friday:The Eureka forecast for Apr 21 is 54 degrees and Partly cloudy. There is 65 percentage chance of rain and 8 mph winds from the North-Northeast. 2  Saturday:The Eureka forecast for Apr 22 is 47 degrees and Light rain. There is 79 percentage chance of rain and 17 mph winds from the Northeast.