The short answer: No.
If you die intestate (leaving no valid Will), Minnesota's intestacy laws exclude ex-spouses. Therefore, an ex-spouse is not entitled to your estate assets. Instead, your assets would be distributed based on the state's intestate succession law: to current spouse, children, parents, siblings, etc. Next of kin.
However, if your divorce decree requires division of marital property and you still have any of that property when you die, your ex would have legal claim based on the decree.
For example: if the decree requires dividing proceeds from selling the house, but you die before the sale is completed, your ex-spouse is entitled to the share of the property, per the terms of the divorce decree. Thus, your ex could make a claim against your estate in probate court.
As you can see, these types of scenarios are governed by the terms in the divorce decree.
Another issue would arise if your divorce is not final at the time of your death. You would still be legally married at that time, and your spouse would be entitled to at least a spousal elective share under Minnesota law. And if you have no valid Will, guess what? The intestacy laws put your spouse at the head of the line for inheriting your estate assets.
If you are divorced and you haven't already done so, it is a good idea to review your financial instruments that have named beneficiaries, such as insurance policies, retirement plans, investments, and assets with payable-on-death provisions such as bank accounts and real estate. Your ex-spouse may still be named as a beneficiary and you may wish to change that. Fortunately, Minnesota law automatically revokes the beneficiary designation of an ex-spouse, so revisiting those instruments is mainly a matter of naming new beneficiaries.
Finally, if you have Power of Attorney or a Health Care Directive that names your ex-spouse as a fiduciary, you may wish to review those documents. Minnesota law also automatically revokes the fiduciary status of an ex-spouse, so revisiting those allows you to choose new fiduciaries.
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If you are recently divorced or are currently in the divorce process, it would be a
good idea to seek out a qualified attorney to discuss your estate
planning needs. Your divorce attorney should have some knowledge of how your estate could be impacted by divorce, and they may be able to help with some of those concerns. However, it would be wise to seek separate estate planning counsel to ensure all of your estate-related issues are addressed and up-to-date.