Legal Question in Landlord & Tenant Law in Minnesota

No - In Minnesota LL's obligations are generally a matter of the terms of the Lease, and that would have to be reviewed by an Attorney to see if it covered this item.

That being said, normally LL's want to update/upgrade carpeting on a schedule they determine, and if you request an inspection, you may get farther than demanding a "legal " right under law.

If it is a health or safety issue , i.e. disgusting smells or holes that you trip on, then I would inform the LL and suggest replacement. Most LL/s want ":happy" tenants, i.e. tenants who willingly pay the rent on time.

There is an obligation of habitability on the part of the LL, but it is vague and hard to pin down, usually requiring a judge's perspective to enforce in many instances.