Mint Moving
7204 W 27th St #222, Minneapolis(651) 382-1081
Open SaturdayWebsite
14 moving companies in and around Minneapolis (within 9 miles) list moving and storage in their own details, 10 of them with their own website. All of them are below, with address and phone number.

Order: moving companies with a working website first, then by how complete their details are. Nobody pays for a spot in this list.
14 of the 45 moving companies in Minneapolis list moving and storage in their own details (31%). Not every company fills in everything, so the real number may be higher.
Nearby: Roseville (3, 5.5 miles), Edina (4, 7.5 miles), Maplewood (3, 13 miles).
This is what the companies list themselves. If in doubt, just ask them.