If you have health insurance through your employer, no, you will not lose it - but you will have to change your plan to remove your spouse. If you get insurance through your spouse's employer, yes, you'll lose coverage.
Luckily, this is a qualifying life event, so if you lose coverage, you don't have to wait for an open enrollment period to get new insurance. You can get new health coverage immediately so you don't have a lapse. Check with your employer, or healthcare.gov, or this page on COBRA insurance.