When the users login into the Sandbox after the Refresh, it will prompt them to setup the MFA again.
Note:
The configuration in Authenticator App won’t be automatically deleted after the Sandbox Refresh. It has to manually deleted before setting up again for the Sandbox after the Refresh.
Previously configured MFA for the Sandbox will be Invalidated due to Org id change.
Note:
Org Id changes after the Salesforce Sandbox Refresh.
If you want to avoid MFA in the Sandbox, do a post refresh activity to remove the MFA Permission from the Profiles and Permission Sets.
Check the following for best practices and more information on this: