you should have your speedometer cable checked. most likely it is
broken. i had a honda civic before for about 5 years when the same
thing happened. the amber engine indicator will always be turned on
until the problem is fixed.
although you can still drive, you won't know if other more fatal engine
problems arise because the engine indicator is turned on.

this site might help you find the right type for your car (i don't work
here, sorry): http://www.hondapartstore.com/Honda_Civic_11203.html

crash.test.dummy