Dodge County Mn Apartments For Rent . Browse photos, get pricing and find the most affordable housing. The average voucher holder contributes $300 towards rent in dodge county. 405 N Mantorville Ave, Kasson, MN Trulia from www.trulia.com How expensive is it to rent an apartment in dodge county, mn? We found 1 apartments for rent in dodge county, mn. Explore 4 apartments for rent in dodge county with rental rates ranging from $695 to $875.