Actually, you can hand wash your silk sheet with the appropriate detergent, if you don’t want to spend money on dry-cleaning.
Wash silk sheets by hand the first few times after your purchase and use. This protects the silk’s sheen and softens the fibers. Use only lukewarm water and a gentle, biodegradable detergent or a detergent specially formulated for silk. Resist the urge to rub the fabric vigorously, and don’t let silk bed sheets soak too long. When removing the excess water from your silk sheets, don’t wring them with your bare hands. Wrap the sheets in a large towel and gently twist.
Note that silk by nature is a strong fabric. Silk sheet set should not be washed in strong detergents that tend to strip away natural features.