The short answer is no, at least for high compression garments over 30mmHg, unless you have been instructed to do so by your doctor. Lighter compression garments like anti-embolism stockings can be worn at night, as well as mild compressions of 8-15mmHg. If you need compression round the clock, your doctor or therapist will probably recommend a different type of compression garment when you sleep, like bandaging or a nightwear garment.
Short stretch bandaging or wrapping is often worn at night by individuals who have lymphedema or chronic edema. This type of compression is very mild when resting. The bandage only provides resistance and significant compression when the underlying muscles are active and pushing against the bandage.
Tribute by Solaris Medical is specifically designed for nighttime wear. Tribute garments can be worn on any part of the body and each garment is custom made. The outer layer is made of a stretchy fabric that provides compression. The interior is filled with foam chips that gently massage the tissues while you sleep, which helps release interstitial fluids and reduce swelling. Tribute garments are very comfortable so they won't interfere with your sleep, and the fabric is specially treated to remove moisture and help keep you cool.
BiaCare makes a similar line of nighttime garments. Their foam and chip sleeves can be worn at night. Both are available in ready-to-wear sizes and custom. In combination with an oversleeve, the foam sleeve provides 10-15mmHg and the chip 15-20mmHg.
Biacare's CompreFit system for legs, can also be worn at night. CompreFit mimics the compression of short stretch bandaging, but is much easier to put on and take off. The calf unit, which includes a boot for the foot, provides compression up to the knee. A thigh unit can be added to provide compression from foot to groin.
Before beginning any nighttime compression regimen, be sure to consult with your doctor or therapist.