To create a Shipping Restriction rule that will be applied only on a specific day of the week, navigate to Magento Admin Panel → Sales → Shipping Restrictions and click on Add Rule. Fill in all of the required fields, as well as the conditions of the restriction, and scroll down to the Days and Time section of the rule to select the days of the week:
You can configure the From/To Time as well to make the restriction even more precise. The Restriction Rule shown below will be triggered only on Saturday from 10 a.m. to 8 p.m: