I believe the law is 7 business days (IMO) but wouldn't gripe about the extra three. Mine only took 7 in Rock County.
Option 1
Fill out a the Minnesota Uniform Firearm Application/Receipt Permit to Purchase/Transfer. Submit the application to your local police chief, or if your municipality does not have a police department, to your county's sheriff. The law enforcement agency will conduct a series of background-related checks to assure you meet eligibility requirements established in state law.
Once those checks are complete, a one-year permit to purchase a handgun in Minnesota will be issued. If you are applying for a permit to transfer the law enforcement agency must notify you of its status within seven days of receipt.
If you are selling a handgun and the buyer has not obtained a permit to purchase, you must notify the local police department or sheriff's office of the potential transaction. Once the law enforcement agency receives the transfer/purchase agreement, the agency has five days to determine the potential buyer's eligibility to possess a handgun.
Option 2
If you want to make a one-time purchase of a handgun from a dealer and you do not have a permit to purchase, you may apply directly at the gun shop where you will purchase the handgun. The gun shop will require you to complete a consent form that allows them to conduct a name and date-of-birth background check to determine your eligibility to purchase a gun. The gun shops are entitled to charge a fee for this service.
From the Minnesota BCA website.