CA requires that you use the same filing status on your CA return that you use on your federal return. Filing MFJ is the best choice for most married couples.

Some complications you need to be aware of:  CA is a community property state.  Therefore income you earn after you become a CA resident will be split equally between you and your husband for tax purposes.  This is important to realize in case you decide to file CA separately, because your husband would have to include his share of the community income on his return.  You become a resident of CA for tax purposes on the day you begin living in your new home in CA.

Additionally, CA taxes non-residents on CA-source income.  Income is "sourced" where the work is actually performed.  Therefore, as @NCperson said, the money your husband earns by working in CA will taxable by CA, even though he'll be working remotely for an out-of-state employer.  So he must keep track of his CA income.  Since he will remain a resident of MN, that income will also be taxable by MN.  He'll be able to take a credit on his MN return for the taxes paid to CA on the income that is taxed by both states, so he won't be double-taxed.  

When you do your tax returns for the year of your move, you'll indicate in the personal info section of TT that you moved to another state during the year.  Your husband will indicate that he lived all year in MN and earned money in another state.  That will prompt TT to produce the correct state tax forms.

One more complication: since it is unlikely that your husband's MN employer will withhold CA taxes from his pay, he may have to look at making quarterly estimated tax payments to CA.  Here are CA's rules on that:  https://www.ftb.ca.gov/pay/estimated-tax-payments.html