Even if no one smokes in bed, a blanket may end up with cigarette smoke odor that lingers long after the smoke dissipates. Smoke clings to just about every surface and fabric in the room, blankets notwithstanding. Instead of just dealing with the obnoxious odor, rid the blanket of that smoke smell using natural odor removers, followed by a good washing.
Air out the blanket over a clothesline outdoors. If no clothesline is available, set two or three chairs in a line and drape the blanket over them so its not folded at all. Airflow helps remove the smoke smell; folds hinder the airflow. If you can't freshen the blanket outdoors, place it in a smoke-free room, stretched across several chairs. Open the windows and turn on the ceiling fan. Use a portable fan to draw air away from the blanket, toward an open window. If the smell persists after several hours, sprinkle the blanket with baking soda and allow it to air out for a few more hours.
Wash the blanket using the temperature and care settings recommended on its tag. Use your usual bleach-free laundry detergent and add 1 cup white vinegar to the wash load as the machine fills with water. Add another cup of vinegar to the water during the rinse cycle. The vinegar removes odors and also helps remove detergent residues. Air-dry the blanket on a clothesline in the shade, if possible, or in the dryer using the lowest heat setting available. Don't use fabric softeners or dryer sheets, as these leave behind a coating that traps odors in the blanket. Skip this step if the blanket is not machine-washable.
Spritz a gentle mist of white vinegar over the blanket if it still smells of cigarette smoke even after airing it out or washing it. Stretch the blanket out over a clothesline or spread it across several chairs to allow it to air dry. Test a corner of the blanket first to ensure the vinegar does not affect the dyes in the blanket; generally, vinegar is safe -- but if the blanket is not color-fast, the colors may bleed.
Treat a nonwashable blanket by placing it in an airtight plastic storage tub. Pour a heap of baking soda or kitty litter onto a paper coffee filter, setting the filter atop the blanket. Seal the lid on the bin, and then place the bin in a sunny location outdoors or within direct sunlight inside, in non-humid conditions. Open the lid every day or so to sniff the blanket, replacing the baking soda or kitty litter as needed. Both baking soda and kitty litter absorb odors well. It may take several days to remove the smoke odor completely.