You can microwave shop towels.
Shop towels can be used in the microwave to cover food with and they will be just fine as long as you keep an eye on the food cooking in the microwave so the shop towels don't burn.
If the microwave is left on too long the shop towels or any other paper towels could burn.
But when used for short amounts of time in the microwave the shop towels or any other paper towels will be just fine.
Almost all paper towels are safe to be used in the microwave.
Paper towels are generally used in microwaves to cover food items or as a plate liner to absorb excess moisture.
Paper towels, wax paper, parchment paper, paper plates and bowls are fine in the microwave.
Brown paper bags are never safe in the microwave because they can't withstand a lot of heat and can catch fire.
Why did my paper towel catch fire in the microwave?
Microwave ovens produce microwaves which cause the molecules in your food, drink and yes your paper towels to vibrate which creates heat.
However, when the paper towel is folded or scrunched up this heat can build up enough to set the paper towel on fire.