There is no good data to show that electro-magnetic fields (EMFs) produced by electric blankets, cell phones and other devices cause cancer. Electric blankets do emit radiation from the movement of electric current through wires. Extensive studies in animals have repeatedly failed to show that low-frequency radiation EMFs cause cancer (Progress in Biophysics and Molecular Biology 2011; 107(3):369-373).

EMFs are classified into:
High-frequency EMFs, such as x-rays and gamma rays, that can damage cells and DNA to cause cancer (CA Cancer J Clin, Mar-April, 2012;62(2):75–100).
Intermediate-frequency EMFs that can damage cells, such as those produced in home microwave ovens (Am J Emerg Med, Jun 31, 2013;31(6):958-63). Long-term exposure to microwaves has been reported to increase risk for cancerous cell changes (Exp Oncol, Jun 23, 2011;33(2):62-70), but microwave ovens are manufactured with extra shielding to reduce leakage. For extra safety, you should not stay close to a microwave oven when it is turned on.
Low-frequency EMFs, such as those from electric appliances, radio waves, MRIs from your doctor, infrared radiation and visible light, have not been shown to damage DNA to cause cancer (Prog Biophys Mol Biol, Dec 2011;107(3):369-73). These include electrical wiring and electrical appliances such as electric blankets, cordless telephones, shavers, hair dryers, radios, television, and laptop computers.

Electric Blankets Appear to Be Safe
I have not been able to find any strong evidence that electric blankets increase risk for cell damage or cancer. I found studies that showed no increased risk for electric blankets causing:
• thyroid cancer (Women Health, Feb 15, 2016; 55(7): 829–841)
• breast cancer (American Journal of Epidemiology, July 1, 2000;152(1): 41–49)
• endometrial cancer (Am J Epidemiol, 2002 Aug 1;156(3):262-7)
I did find a 20-year study associating electric blankets with a slightly increased risk for endometrial cancer (Eur J of Can Preven, Jun, 2007;16(3):243-50), and another study of increased risk for miscarriage with exposure to non-ionizing radiation (Scientific Reports, Dec 13, 2017;7(17541)).

My Recommendations
At this time I can find no good evidence that electric blankets increase risk for cell damage or cancer. However, increasing distance between your body and the electric blanket markedly decreases your exposure to electromagnetic waves (Occupational and Environmental Medicine, 2009; 66(8):550-6). Just moving the electric blanket 10 centimeters from your body decreases electromagnetic waves by more than 90 percent (Scientific Reports, Dec 13, 2017;7(17541:). I have no evidence that you need to do this, but putting the electric blanket over a sheet and another blanket will markedly decrease your exposure to electromagnetic waves. The safety instructions that come with these blankets remind you not to put any other blankets or covers on top of an electric blanket.