I did not find any laws around ammunition, just that the firearm had to be unloaded.
624.714 Carrying Of Weapons Without Permit; Penalties.
https://www.revisor.mn.gov/statutes/?id=624.714Subd. 9 A permit to carry is not required of a person:
(5) to transport a pistol in a motor vehicle, if the pistol is unloaded,
contained in a closed and fastened case, gunbox, or securely tied package.
97B.045 Transportation of Firearms.
https://www.revisor.mn.gov/statutes?id=97B.045Subdivision 1.Restrictions.
A person may not transport a firearm in a motor vehicle unless the firearm is:
(1) unloaded and in a gun case expressly made to contain a firearm,
and the case fully encloses the firearm by being zipped, snapped, buckled, tied, or otherwise fastened,
and without any portion of the firearm exposed;
(2) unloaded and in the closed trunk of a motor vehicle