What type of light is being turned on? If it is a CFL (Compact Fluorescent) then the electronics are probably emitting EMI (Electro-Magnetic Interference) due to either a fault or poor design. It might also be the light switch itself, arcing (thus causing EMI) when it is being turned on or off.
HDMI cables are supposed to have shielding incorporated to prevent EMI from causing a problem.
Suggest you try to isolate the problem by either replacing the HDMI cable and/or the light (try a different brand - I have had 2 of the same type of light (CFL), in the room, but different brands, one causes interference when being turned on, pixellation and sound glitches on my TV when the input source is the antenna. The antenna is in the ceiling space about 5' away from the light - no problems on HDMI though, the other no problems.
If it is neither of the above, you can test the light switch by using a portable radio.Tune it off-station on the AM band, then hold it near the switch, then turn the switch on and off. If there is a problem you will hear it in the radio as a burst of interference each time the switch is closed or opened. If there is, the switch will need to be replaced. You can try this near the light as well, although if you do this before you have changed the light you still mightn't know if it is the light or the switch, which is at fault.
Be aware of the dangerous voltages associated with lights and power in the premises if you need to replace the light switch. If uncertain yourself, call in a professional.