You don’t need call a plumber right away, just use what you have in your house, hopefully you have it on hand, if not it is worth the trip to the store because it costs very little money!
First remove any standing water. Pour about a 1/2 box of baking soda in the drain. Then pour in about a 1/2 cup of white vinegar. The mixture should sit in the drain for about to 20 minutes. After 20 minutes pour about 4 quarts of very hot or boiling water down the drain. This should unstop the drain. If not, plunge a few times (yes a toilet plunger really works). If it doesn’t work the first time try it the second time. It Run the disposal and water as well, it should be working. Rinse with cool water. Please don’t do this in a toilet, it's for sinks drains only.