First and foremost… don't panic!
No dry cleaning is needed! Start by testing a small, discrete area on the fabric with a dab of common laundry soap and cold water using a clean, soft white piece of lint-free fabric. If all is fine and well (which it should be), throw it in the washing machine on a gentle cycle with cold water. Lay flat or hang until dry. If some wrinkling does occur, don’t fret! Use a handheld steamer to clean up the final touches.