No. You do not need to file neither an Arizona nor Minnesota nonresident tax return.
Individuals must file if they are: Single AND gross income is more than: $13,850
Married filing joint AND $27,700
Married filing separate AND $13,850
Head of household AND $20,800
For non-resident individuals the threshold numbers above are prorated based on the individual's Arizona gross income to their federal adjusted gross income.
Arizona Department of Revenue - Individual Income Tax Information
You are required to file a Minnesota income tax return if your Minnesota gross income meets the minimum filing requirement ($13,825 for 2023).
Minnesota Department of Revenue - Nonresidents